Didier Pilod

Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory

The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers equation improves (enlarges) the space of resolution of the local Cauchy problem. More generally we will review several problems arising from weak dispersive perturbations of nonlinear hyperbolic equations or systems.

Well-posedness for the fifth-order KdV equation in the energy space

We prove that the initial value problem (IVP) associated to the fifth order KdV equation {equation} \label{05KdV} \partial_tu-\alpha\partial^5_x u=c_1\partial_xu\partial_x^2u+c_2\partial_x(u\partial_x^2u)+c_3\partial_x(u^3), {equation} where

Well-Posedness of Strongly Dispersive Two-Dimensional Surface Wave Boussinesq Systems

x \in \mathbb R

Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons

,

Global Well-Posedness and Limit Behavior for a Higher-Order Benjamin-Ono Equation

t \in \mathbb R

The Cauchy Problem for the Fractional Kadomtsev--Petviashvili Equations

,

The Cauchy problem for the Benjamin–Ono equation in L2 revisited

u=u(x,t)

On the Cauchy problem for higher-order nonlinear dispersive equations

is a real-valued function and

Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications

\alpha, \ c_1, \ c_2, \ c_3

Sharp well-posedness results for the Kuramoto-Velarde equation

are real constants with