Large data scattering for the defocusing supercritical generalized KdV equation

Abstract

We consider the defocusing supercritical generalized Korteweg-de Vries (gKdV) equation ${\partial }_{t}u+{\partial }_x^{3}u-{\partial }_x(u^{k+1})=0$, where $k>4$ is an even integer number. We show that if the initial data $u_0$ belongs to $H^1$ then the corresponding solution is global and scatters in $H^1$. Our method of proof is inspired on the compactness method introduced by C. Kenig and F. Merle.

36 pages

References in corpus (3)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Nonlinear Profile Decomposition and the Concentration Phenomenon for Supercritical Generalized KdV Equations

Cited by in corpus (2)

• Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schrödinger equations
• Scattering for Defocusing generalized Benjamin-Ono Equation in the Energy Space