credit: Coulorbox
Research Interests
Analysis and Partial Differential Equations
My research is centered on mathematical analysis and partial differential equations. It focuses mainly on the study of properties of nonlinear dispersive evolution equations arising in mathematical physics and fluid mechanics. More precisely, I am interested in the following aspects of nonlinear dispersive equations:
Well-posedness in connexion with harmonic analysis;
Construction, stability and collision of solitons, multi-solitons or other special solutions;
Long time dynamics: scattering and formation of singularities (blow-up);
Unique continuation.
Most of my papers are available on the arXiv or on Googles Scholar
Preprints
Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation, preprint (2024), 72 pages, joint with Frédéric Valet.
Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation, preprint (2024), 32 pages, joint with Frédéric Valet.
On the Benjamin and related equations, preprint (2023), 26 pages, joint with Christian Klein, Felipe Linares, and Jean-Claude Saut.
Intermediate long wave equation in negative Sobolev spaces, preprint (2023), 15 pages, joint with Andreia Chapouto, Justin Forlano, Guopeng Li and Tadahiro Oh.
Deep-water limit of the intermediate long wave equation in L^2, preprint (2023), 26 pages, joint with Andreia Chapouto, Guopeng Li and Tadahiro Oh.
Well-posedness for the extended Schrödinger-Benjamin-Ono system, to appear in Vietnam Journal of Mathematics, preprint (2023), 22 pages, joint with Felipe Linares and Argenis Mendez.
Finite point blowup for the critical generalized Korteweg-de Vries equation, to appear in Annali Scuola Normale Superiore - Classe di Scienze, preprint (2021), 41 pages, joint with Yvan Martel.
Publications
Unconditional uniqueness for the Benjamin-Ono equation, Pure&Applied Analysis, 5 (2023), 285–322, joint with Razvan Mosincat.
Global well-posedness and scattering for the Dysthe equation in L^2, J. Math. Pures Appl., 149 (2021), 73–97, joint with Razvan Mosincat and Jean-Claude Saut.
Dispersive estimates for full dispersion KP equations, J. Math. Fluid Mech., 23 (2021), paper no. 25, 24 pp, joint with Jean-Claude Saut, Sigmund Selberg and Achenef Tesfahun
Full family of flattening solitary waves for the mass critical generalized KdV equation, Comm. Math. Phys., 378, (2020),1011-1080, joint with Yvan Martel.
On the unique continuation of solutions to non-local non-linear dispersive equations, Comm. Part. Diff. Eq., 45 (2020), no. 8, 872-886, joint with Carlos Kenig, Gustavo Ponce and Luis Vega.
On the local well-posedness for a full dispersion Boussinesq system with surface tension, Proc. Amer. Math. Soc., 147 (2019), 2545-2559, joint with Henrik Kalisch.
On unconditional well-posedness for the periodic modified Korteweg-De Vries equation, J. Math. Soc. Japan, 71 (2019), no. 1, 147–201, joint with Luc Molinet and Stéphane Vento.
On well-posedness for some dispersive perturbations of Burgers' equation, Ann. Inst. H. Poincaré An. Non Lin., 35 (2018), no. 7, 1719–1756, joint with Luc Molinet and Stéphane Vento.
Unconditional uniqueness for the modified Korteweg- de Vries equation on the line, Rev. Mat. Iber., 34 (2018), no. 4, 1563–1608, joint with Luc Molinet and Stéphane Vento.
The Cauchy problem for the fractional Kadomtsev-Petviashvili equations, SIAM J. Math. Analysis, 50 (2018), 3172-3209, joint with Felipe Linares, and Jean-Claude Saut.
On Whitham and related equations, Studies Appl. Math., 140 (2018), 133-177, joint with Christian Klein, Felipe Linares, and Jean-Claude Saut.
Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation, Mathematische Annalen, 369 (2017), 153-245, joint with Yvan Martel.
Local well-posedness for the KdV hierarchy at high regularity, Adv. Diff. Eq., 21 (2016) 801-836, joint with Carlos Kenig.
Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons, Arch. Rat. Mech. Anal., 220(2016), 639-710, joint with Raphaël Côte, Claudio Muñoz, and Gideon Simpson.
Remarks on the orbital stability of ground state solutions of fKdV e relative equations, Adv. Diff. Eq., 20 (2015), 835-858, joint with Felipe Linares, and Jean-Claude Saut.
Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications, Ann. Inst. H. Poincaré An. Non Lin., 32 (2015), 347-371, joint with Luc Molinet.
Well-posedness for the fifth-order KdV equation in the energy space, Trans AMS, 367 (2015), 2555-2612 , joint with Carlos Kenig.
Dispersive perturbations of Burgers and hyperbolic equations I: local theory, SIAM J. Math. Analysis, 46 (2014), 1505-1537, joint with Felipe Linares, and Jean-Claude Saut.
Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation, Comm. PDE, 37 (2012), 2050-2080, joint with Luc Molinet.
Well-posednesss of strongly dispersive two-dimensional surface waves Boussinesq systems, SIAM J. Math. Analysis, 44 (2012), 4195-4221, joint with Felipe Linares and Jean-Claude Saut.
The Cauchy problem for the Benjamin-Ono equation in L^2 revisited, Analysis&PDE, 5 (2012) 365-395, joint with Luc Molinet.
Well-posedness for a higher-order Benjamin-Ono equation, J. Diff. Eq., 250 (2011) 450-475. joint with Felipe Linares and Gustavo Ponce.
Local well-posedness for the nonlocal nonlinear Schrödinger equation below the energy space, Adv. Diff. Eq., 15 (2010) 925-952, joint with Roger Moura.
Stability of solitary-wave solutions to the Hirota-Satsuma equation, Disc. Cont. Dyn. Syst. A, 27 (2010) 1397-1413, joint with Jerry Bona.
Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system, Comm. Pure Appl. Anal., 8 (2009), 815-844, joint with Jaime Angulo and Carlos Matheus.
Well-posedness for Hirota-Stasuma's equation, Diff. Int. Eq., 21 (2008) 1177-1192, joint with Rafael Iório.
On the Cauchy problem for higher-order nonlinear dispersive equations, J. Diff. Eq., 245 (2008) 2055-2077.
Sharp well-posedness results for the Kuramoto-Velarde equation, Comm. Pure Appl. Anal., 7(2008) 867-881.
Proceedings
Asymptotic stability of Zakharov-Kuznetsov solitons, Séminaire Laurent-Schwartz. 2014-2015. Exp. 13, 12 pages. École Polytechnique, Palaiseau (2016).
Last update: March 14, 2024