Didier Pilod

Research

Research Interests


Partial Differential Equations

Nonlinear Dispersive Equations:

  • Well-posedness
  • Stability and asymptotic stability
  • Blow-up

  • Most of my papers are available on the arXiv

    Preprints


    1. Full family of flattening solitary waves for the mass critical generalized KdV equation, preprint (2019), 62 pages, joint with Yvan Martel.

    Publications


    1. 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.
    2. On unconditional well-posedness for the periodic modified Korteweg-De Vries equation, J. Math. Soc. Japan (2018),71 (2019), no. 1, 147–201, joint with Luc Molinet and Stéphane Vento.
    3. 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.
    4. 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.
    5. 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.
    6. On Whitham and related equations, Studies Appl. Math., 140 (2018), 133-177, joint with Christian Klein, Felipe Linares, and Jean-Claude Saut.
    7. Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation, Mathematische Annalen, 369 (2017), 153-245, joint with Yvan Martel.
    8. Local well-posedness for the KdV hierarchy at high regularity, Adv. Diff. Eq., 21 (2016) 801-836, joint with Carlos Kenig.
    9. 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.
    10. 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.
    11. 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.
    12. Well-posedness for the fifth-order KdV equation in the energy space, Trans AMS, 367 (2015), 2555-2612 , joint with Carlos Kenig.
    13. 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.
    14. Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation, Comm. PDE, 37 (2012), 2050-2080, joint with Luc Molinet.
    15. 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.
    16. The Cauchy problem for the Benjamin-Ono equation in L^2 revisited, Analysis&PDE, 5 (2012) 365–395, joint with Luc Molinet.
    17. Well-posedness for a higher-order Benjamin-Ono equation, J. Diff. Eq., 250 (2011) 450-475. joint with Felipe Linares and Gustavo Ponce.
    18. Local well-posedness for the nonlocal nonlinear Schrödinger equation below the energy space Adv. Diff. Eq., 15 (2010) 925-952, joint with Roger Moura.
    19. Stability of solitary-wave solutions to the Hirota-Satsuma equation, Disc. Cont. Dyn. Syst. A, 27 (2010) 1397-1413, joint with Jerry Bona.
    20. 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.
    21. Well-posedness for Hirota-Stasuma's equation, Diff. Int. Eq., 21 (2008) 1177-1192, joint with Rafael Iório.
    22. On the Cauchy problem for higher-order nonlinear dispersive equations, J. Diff. Eq., 245 (2008) 2055-2077.
    23. Sharp well-posedness results for the Kuramoto-Velarde equation, Comm. Pure Appl. Anal., 7 (2008) 867-881.
    Last Update: June 2nd, 2019