2026
Well-posedness and finite element approximation of the electrostatic shear Alfvén wave equations
2026
Long finite time bubble trees for two co-rotational wave maps
2026
Construction of Blow-Up Solutions for the Focusing Energy-Critical Nonlinear Wave Equation in $\mathbb {R}^4$ and $\mathbb {R}^5$
Annales Henri Poincaré. 2026. DOI : 10.1007/s00023-026-01664-5.2025
Wave maps from circle to Riemannian manifold: global controllability is equivalent to homotopy
2025
The cubic NLS on the line with an inverse square potential
2025
Global Controllability and Stabilization of the Wave Maps Equation From a Circle to a Sphere
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. 2025. Vol. 64, num. 4. DOI : 10.1007/s00526-025-02961-3.Concentric bubbles concentrating in finite time for the energy critical Wave Maps equation
2025
Decomposable and Indecomposable Continua
Connected Sets in Global Bifurcation Theory; Cham: Springer Nature Switzerland, 2025. p. 63 – 79.Connected Sets in Global Bifurcation Theory
Cham, Switzerland: Springer Science and Business Media B.V., 2025.Congestion Points
Connected Sets in Global Bifurcation Theory; Cham: Springer Nature Switzerland, 2025. p. 45 – 61.Set Theory Foundations
Connected Sets in Global Bifurcation Theory; Cham: Springer Nature Switzerland, 2025. p. 9 – 10.Pathological Examples
Connected Sets in Global Bifurcation Theory; Cham: Springer Nature Switzerland, 2025. p. 81 – 93.Types of Connectedness
Connected Sets in Global Bifurcation Theory; Cham: Springer Nature Switzerland, 2025. p. 33 – 43.2024
Finite time blow up for the energy critical Zakharov system I: approximate solutions
2024
FINITE TIME BLOW UP FOR THE ENERGY CRITICAL ZAKHAROV SYSTEM II: EXACT SOLUTIONS
2024
Stability of the Faber-Krahn inequality for the short-time Fourier transform
Inventiones Mathematicae. 2024. DOI : 10.1007/s00222-024-01248-2.Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations
Lausanne, EPFL, 2024.GLOBAL RESULTS FOR A CAUCHY PROBLEM RELATED TO BIHARMONIC WAVE MAPS
Pure and Applied Analysis. 2024. Vol. 6, num. 3, p. 657 – 691. DOI : 10.2140/paa.2024.6.657.2023
ALMOST SURE SCATTERING OF THE ENERGY-CRITICAL NLS IN d > 6
Communications On Pure And Applied Analysis. 2023. Vol. 22, num. 10, p. 3165 – 3199. DOI : 10.3934/cpaa.2023106.Global controllability and stabilization of the wave Maps equation from a circle to a sphere
2023
Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls
Journal Of Differential Equations. 2023. Vol. 355, p. 193 – 218. DOI : 10.1016/j.jde.2023.01.026.Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets
Lausanne, EPFL, 2023.Scattering Map for the Vlasov–Poisson System
Peking Mathematical Journal. 2023. Vol. 6, p. 365 – 392. DOI : 10.1007/s42543-021-00041-x.BOUNDARY STABILIZATION OF THE FOCUSING NLKG EQUATION NEAR UNSTABLE EQUILIBRIA: RADIAL CASE
Pure and Applied Analysis. 2023. Vol. 5, num. 4, p. 833 – 894. DOI : 10.2140/paa.2023.5.833.Global Well-Posedness For Half-Wave Maps With S-2 And H-2 Targets For Small Smooth Initial Data
Communications On Pure And Applied Analysis. 2023. Vol. 22, num. 1, p. 127 – 166. DOI : 10.3934/cpaa.2022148.2022
Fredholm transformation on Laplacian and rapid stabilization for the heat equation
Journal Of Functional Analysis. 2022. Vol. 283, num. 12, p. 109664. DOI : 10.1016/j.jfa.2022.109664.Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps
Proceedings of the American Mathematical Society. 2022. DOI : 10.1090/proc/16100.A b-symplectic slice theorem
Bulletin of the London Mathematical Society. 2022. DOI : 10.1112/blms.12713.Semi-global controllability of a geometric wave equation
Pure and Applied Mathematics Quarterly. 2022. DOI : 10.48550/arXiv.2205.00915.b-Structures on Lie groups and Poisson reduction
Journal Of Geometry And Physics. 2022. Vol. 175, p. 104471. DOI : 10.1016/j.geomphys.2022.104471.Fully Localised Three-Dimensional Gravity-Capillary Solitary Waves on Water of Infinite Depth
Journal Of Mathematical Fluid Mechanics. 2022. Vol. 24, num. 2, p. 55. DOI : 10.1007/s00021-022-00684-5.Stabilization of the linearized water tank system
Archive for Rational Mechanics and Analysis. 2022. Vol. 244, p. 1019 – 1097. DOI : 10.1007/s00205-022-01778-0.Mass-Energy threshold dynamics for dipolar Quantum Gases
Communications In Mathematical Sciences. 2022. Vol. 20, num. 1, p. 165 – 200. DOI : 10.4310/CMS.2022.v20.n1.a5.On the asymptotic behavior of solutions to the Vlasov-Poisson system
International Mathematics Research Notices. 2022. num. 12, p. 8865 – 8889. DOI : 10.1093/imrn/rnab155.Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$
Memoirs of the AMS. 2022. Vol. 278. DOI : 10.1090/memo/1369.2021
Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates
Calculus Of Variations And Partial Differential Equations. 2021. Vol. 60, num. 6, p. 229. DOI : 10.1007/s00526-021-02096-1.Small-time global stabilization of the viscous Burgers equation with three scalar controls
Journal de Mathématiques Pures et Appliquées. 2021. Vol. 151, p. 212 – 256. DOI : 10.1016/j.matpur.2021.03.001.Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
Electronic Journal Of Combinatorics. 2021. Vol. 28, num. 3, p. P3.1. DOI : 10.37236/9780.Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case
Communications in Mathematical Physics. 2021. Vol. 385, p. 1741 – 1769. DOI : 10.1007/s00220-021-04117-8.Small data global regularity for half-wave maps in n=4 dimensions
Communications in Partial Differential Equations. 2021. Vol. 46, num. 12, p. 2305 – 2324. DOI : 10.1080/03605302.2021.1936021.Ill-posedness of the quasilinear wave equation in the space 𝐻7/4(ln𝐻)−𝛽in ℝ2+1
Lausanne, EPFL, 2021.Randomization improved Strichartz estimates and global well-posedness for supercritical data
Annales de l’Institut Fourier. 2021. Vol. 71, num. 5, p. 1929 – 1961. DOI : 10.5802/aif.3448.Mixing and diffusion for rough shear flows
Ars Inveniendi Analytica. 2021. num. 2. DOI : 10.15781/83fc-j334.2020
The Surface Quasi-geostrophic Equation With Random Diffusion
International Mathematics Research Notices. 2020. Vol. 2020, num. 23, p. 9370 – 9385. DOI : 10.1093/imrn/rny261.Small-time local stabilization of the two dimensional incompressible Navier-Stokes equations
2020
Probabilistic small data global Well-Posedness of the energy-critical Maxwell-Klein-Gordon equation
Archive for Rational Mechanics and Analysis. 2020.Quantitative rapid and finite time stabilization of the heat equation
2020
A stability theory beyond the co-rotational setting for critical wave maps blow up
2020.Enhanced Dissipation in the Navier-Stokes Equations Near the Poiseuille Flow
Communications In Mathematical Physics. 2020. Vol. 378, p. 987 – 1010. DOI : 10.1007/s00220-020-03814-0.Large data scattering for NLKG on waveguide R-d x T
Journal Of Hyperbolic Differential Equations. 2020. Vol. 17, num. 2, p. 355 – 394. DOI : 10.1142/S0219891620500095.Boundary Stabilization of Focusing NLKG near Unstable Equilibria: Radial Case
2020
On long time behavior of solutions to nonlinear dispersive equations
Lausanne, EPFL, 2020.On the stability of blowup solutions for the critical corotational wave-map problem
Duke Mathematical Journal. 2020. Vol. 169, num. 3, p. 435 – 532. DOI : 10.1215/00127094-2019-0053.Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations
2020
Stability of slow blow-up solutions for the critical focussing nonlinear wave equation on $\mathbb{R}^{3+1}$
2020. Conference on Mathematics of Wave Phenomena 2018, Karlsruhe, Germany, July 23-28, 2018. p. 69 – 88. DOI : 10.1007/978-3-030-47174-3_5.On the stabilizing effect of rotation in the 3d Euler equations
2020.2019
Cost for a controlled linear KdV equation
ESAIM: Control, Optimisation and Calculus of Variations. 2019. Vol. 27, p. S21. DOI : 10.1051/cocv/2020066.Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
Nonlinearity. 2019. Vol. 33, num. 9, p. 4818 – 4836. DOI : 10.1088/1361-6544/ab8fb5.On Classical Global Solutions of Nonlinear Wave Equations with Large Data
International Mathematics Research Notices. 2019. Vol. 2019, num. 19, p. 5859 – 5913. DOI : 10.1093/imrn/rnx086.Control and stabilization of the periodic fifth order Korteweg-de Vries equation
Esaim-Control Optimisation And Calculus Of Variations. 2019. Vol. 25, p. 38. DOI : 10.1051/cocv/2018033.Asymptotic dynamic for dipolar Quantum Gases below the ground state energy threshold
Journal of Functional Analysis. 2019. Vol. 277, num. 6, p. 1958 – 1998. DOI : 10.1016/j.jfa.2019.04.005.Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential
Journal De Mathematiques Pures Et Appliquees. 2019. Vol. 123, p. 1 – 40. DOI : 10.1016/j.matpur.2019.01.002.Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration
Analysis & Pde. 2019. Vol. 12, num. 5, p. 1225 – 1258. DOI : 10.2140/apde.2019.12.1225.On large future-global-in-time solutions to energy-supercritical nonlinear wave equation
2019. AMS-MAA Joint Mathematics Meeting on Spectral Calculus and Quasilinear Partial Differential Equations, and PDE Analysis on Fluid Flows, Atlanta, GA, Jan 04-07, 2017. p. 187 – 214. DOI : 10.1090/conm/725/14559.Local Well-Posedness And Blow-Up For The Half Ginzburg-Landau-Kuramoto Equation With Rough Coefficients And Potential
Discrete & Continuous Dynamical Systems. 2019. Vol. 39, num. 5, p. 2661 – 2678. DOI : 10.3934/dcds.2019111.Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case
New Tools for Nonlinear PDEs and Application; Springer Nature Switzerland, 2019. p. 179 – 202.Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach
Lausanne, EPFL, 2019.2018
Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations
Nonlinearity. 2018. Vol. 31, num. 4, p. 1441 – 1460. DOI : 10.1088/1361-6544/aaa10d.Convergence To Stratified Flow For An Inviscid 3D Boussinesq System
Communications In Mathematical Sciences. 2018. Vol. 16, num. 6, p. 1713 – 1728. DOI : 10.4310/CMS.2018.v16.n6.a10.On the well-posedness of the inviscid SQG equation
JOURNAL OF DIFFERENTIAL EQUATIONS. 2018. Vol. 264, num. 4, p. 2660 – 2683. DOI : 10.1016/j.jde.2017.10.032.On the well-posedness of the inviscid 2D Boussinesq equation
Zeitschrift für angewandte Mathematik und Physik (ZAMP). 2018. Vol. 69, num. 4, p. 103. DOI : 10.1007/s00033-018-0998-6.Concentration compactness for critical radial wave maps
Annals of PDE. 2018. Vol. 4, p. 8. DOI : 10.1007/s40818-018-0045-0.ON THE GLOBAL STABILITY OF A BETA-PLANE EQUATION
ANALYSIS AND PDE. 2018. Vol. 11, num. 7, p. 1587 – 1624. DOI : 10.2140/apde.2018.11.1587.On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$
Memoirs of the American Mathematical Society. 2018. Vol. 267, num. 1301. DOI : 10.1090/memo/1301.Small data global regularity for half-wave maps
Analysis & PDE. 2018. Vol. 11, num. 3, p. 661 – 682. DOI : 10.2140/apde.2018.11.661.A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension
Archive for Rational Mechanics and Analysis. 2018. Vol. 228, num. 3, p. 773 – 820. DOI : 10.1007/s00205-017-1205-1.2017
Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations
Communications in Mathematical Physics. 2017. Vol. 353, num. 3, p. 1201 – 1216. DOI : 10.1007/s00220-017-2846-5.Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy
Annals Of Mathematics. 2017. Vol. 185, num. 3, p. 831 – 893. DOI : 10.4007/annals.2017.185.3.3.A Class Of Large Global Solutions For The Wave-Map Equation
Transactions Of The American Mathematical Society. 2017. Vol. 369, num. 4, p. 2747 – 2773. DOI : 10.1090/tran/6805.$A$-free Rigidity and Applications to the Compressible Euler System
Annali Di Matematica Pura Ed Applicata. 2017. Vol. 196, num. 4, p. 1557 – 1572. DOI : 10.1007/s10231-016-0629-9.Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$
Journal d’Analyse Mathematique. 2017. Vol. 133, p. 91 – 131. DOI : 10.1007/s11854-017-0029-0.2016
Eigenfunction expansions of ultradifferentiable functions and ultradistributions
Transactions Of The American Mathematical Society. 2016. Vol. 368, num. 12, p. 8481 – 8498. DOI : 10.1090/tran/6765.An overview of some recent results on the Euler system of isentropic gas dynamics
Bulletin Of The Brazilian Mathematical Society. 2016. Vol. 47, num. 1, p. 241 – 253. DOI : 10.1007/s00574-016-0135-0.Stability of stationary wave maps from a curved background to a sphere
Discrete & Continuous Dynamical Systems. 2016. Vol. 36, num. 7, p. 3857 – 3909. DOI : 10.3934/dcds.2016.36.3857.Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$
Transactions Of The American Mathematical Society. 2016. Vol. 368, num. 8, p. 5621 – 5654. DOI : 10.1090/tran/6524.On the well-posedness of the Holm-Staley b-family of equations
Journal Of Nonlinear Mathematical Physics. 2016. Vol. 23, num. 2, p. 213 – 233. DOI : 10.1080/14029251.2016.1161261.On a Lagrangian Formulation of the Incompressible Euler Equation
Journal Of Partial Differential Equations. 2016. Vol. 29, num. 4, p. 320 – 359. DOI : 10.4208/jpde.v29.n4.5.A vector field method on the distorted Fourier side and decay for wave equations with potentials
Memoirs of the American Mathematical Society. 2016. Vol. 241, num. 1142-3/4, p. 1 – 80. DOI : 10.1090/memo/1142.2015
On global regularity for systems of nonlinear wave equations with the null-condition
Dynamics of Partial Differential Equations. 2015. Vol. 12, num. 2, p. 115 – 125. DOI : 10.4310/DPDE.2015.v12.n2.a2.Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation
Annals of PDE. 2015. Vol. 1, num. 5, p. 5/1 – 208. DOI : 10.1007/s40818-015-0004-y.Weyl Transforms for H-Type Groups?
Journal of Pseudo-differential Operators And Applications. 2015. Vol. 6, num. 1, p. 11 – 19. DOI : 10.1007/s11868-014-0106-4.Optimal polynomial blow up range for critical wave maps
Communications on Pure and Applied Analysis. 2015. Vol. 14, num. 5, p. 1705 – 1741. DOI : 10.3934/cpaa.2015.14.1705.Center-stable manifold of the ground state in the energy space for the critical wave equation
Mathematische Annalen. 2015. Vol. 361, num. 1-2, p. 1 – 50. DOI : 10.1007/s00208-014-1059-x.Optimal polynomial blow up range for critical wave maps
Lausanne, EPFL, 2015.Global Ill-Posedness of the Isentropic System of Gas Dynamics
Communications on Pure and Applied Mathematics. 2015. Vol. 68, num. 7, p. 1157 – 1190. DOI : 10.1002/cpa.21537.Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space
Duke Mathematical Journal. 2015. Vol. 165, num. 4, p. 723 – 791. DOI : 10.1215/00127094-3167383.Instability of type II blow up for the quintic nonlinear wave equation on $\mathbb{R}^{3+1}$
Bulletin de la Société Mathématique de France. 2015. Vol. 143, num. 2, p. 339 – 355. DOI : 10.24033/bsmf.2690.Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy
Duke Mathematical Journal. 2015. Vol. 164, num. 6, p. 973 – 1040. DOI : 10.1215/00127094-2885982.2014
Stability and instability of expanding solutions to the Lorentzian constant-positive-mean-curvature flow
2014
A counterexample to well-posedness of entropy solutions to the compressible Euler system
Journal Of Hyperbolic Differential Equations. 2014. Vol. 11, num. 3, p. 493 – 519. DOI : 10.1142/S0219891614500143.Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$
MICHIGAN MATHEMATICAL JOURNAL. 2014. Vol. 63, num. 3, p. 451 – 501. DOI : 10.1307/mmj/1409932630.Nondispersive Decay For The Cubic Wave Equation
Analysis & Pde. 2014. Vol. 7, num. 2, p. 461 – 495. DOI : 10.2140/apde.2014.7.461.Full blow-up range for co-rotaional wave maps to surfaces of revolution
2014
Liouville’s theorem and Laurent Series Expansions for Solutions of the Heat Equation
Journal of Pseudo-Differential Operators and Applications. 2014. Vol. 5, num. 4, p. 539 – 547. DOI : 10.1007/s11868-014-0103-7.Threshold phenomenon for the quintic wave equation in three dimensions
Communications in Mathematical Physics. 2014. Vol. 327, num. 1, p. 309 – 332. DOI : 10.1007/s00220-014-1900-9.Stable self-similar blowup in energy supercritical Yang-Mills theory
Mathematische Zeitschrift. 2014. Vol. 278, num. 3-4, p. 1005 – 1032. DOI : 10.1007/s00209-014-1344-0.On the energy dissipation rate of solutions to the compressible isentropic Euler system
Archive for Rational Mechanics and Analysis. 2014. Vol. 214, num. 3, p. 1019 – 1049. DOI : 10.1007/s00205-014-0771-8.Stable blow up dynamics for energy supercritical wave equations
Transactions Of The American Mathematical Society. 2014. Vol. 366, num. 4, p. 2167 – 2189. DOI : 10.1090/S0002-9947-2013-06038-2.On type I blow up formation for the critical NLW
Communications in Partial Differential Equations. 2014. Vol. 39, num. 9, p. 1718 – 1728. DOI : 10.1080/03605302.2013.861847.2013
Nondispersive solutions to the $L^2$-critical half-wave equation
Archive for Rational Mechanics and Analysis. 2013. Vol. 209, num. 1, p. 61 – 129. DOI : 10.1007/s00205-013-0620-1.A comment on the construction of the maximal globally hyperbolic Cauchy development
Journal Of Mathematical Physics. 2013. Vol. 54, num. 11, p. 113511. DOI : 10.1063/1.4833375.Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space
Memoirs Of The American Mathematical Society. 2013. Vol. 223, num. 1047, p. 1 – 99. DOI : 10.1090/S0065-9266-2012-00566-1.Global dynamics away from the ground state for the energy-critical nonlinear wave equation
AMERICAN JOURNAL OF MATHEMATICS. 2013. Vol. 134, num. 4, p. 935 – 965. DOI : 10.1353/ajm.2013.0034.Nonscattering solutions and blowup at infinity for the critical wave equation
Mathematische Annalen. 2013. Vol. 357, num. 1, p. 89 – 163. DOI : 10.1007/s00208-013-0898-1.Global dynamics of the nonradial energy-critical wave equation above the ground state energy
Discrete & Continuous Dynamical Systems. 2013. Vol. 33, num. 6, p. 2423 – 2450. DOI : 10.3934/dcds.2013.33.2423.Non-existence of multiple-black-hole solutions close to Kerr-Newman
Communications In Mathematical Physics. 2013. Vol. 325, num. 3, p. 965 – 996. DOI : 10.1007/s00220-013-1837-4.A codimension two stable manifold of near soliton equivariant wave maps
Analysis & PDE. 2013. Vol. 6, num. 4, p. 829 – 857. DOI : 10.2140/apde.2013.6.829.2012
Stable self-similar blow up for energy subcritical wave equations
Dynamics Of Partial Differential Equations. 2012. Vol. 9, num. 1, p. 63 – 87. DOI : 10.4310/DPDE.2012.v9.n1.a3.Blow Up Construction and Stability of Stationary Maps
Lausanne, EPFL, 2012.Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity
Communications in Partial Differential Equations. 2012. Vol. 37, num. 4, p. 647 – 689. DOI : 10.1080/03605302.2011.643437.On stable self-similar blow up for equivariant wave maps: The linearized problem
Annales Henri Poincaré. 2012. Vol. 13, num. 1, p. 103 – 144. DOI : 10.1007/s00023-011-0125-0.Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials
Annales Henri Poincaré. 2012. Vol. 13, num. 6, p. 1371 – 1426. DOI : 10.1007/s00023-011-0155-7.A positive mass theorem for two spatial dimensions
2012