Electron. J. Diff. Equ., Vol. 2015 (2015), No. 141, pp. 1-24.

Cauchy problems for fifth-order KdV equations in weighted Sobolev spaces

Eddye Bustamante, Jose Jimenez, Jorge Mejia

Abstract:
In this work we study the initial-value problem for the fifth-order Korteweg-de Vries equation
$$ \partial_{t}u+\partial_{x}^{5}u+u^k\partial_{x}u=0, \quad x,t\in \mathbb{R}, \; k=1,2, $$
in weighted Sobolev spaces $H^s(\mathbb{R})\cap L^2(\langle x \rangle^{2r}dx)$. We prove local and global results. For the case $k=2$ we point out the relationship between decay and regularity of solutions of the initial-value problem.

Submitted March 29, 2015. Published May 21, 2015.
Math Subject Classifications: 35Q53, 37K05.
Key Words: Nonlinear dispersive equations; weighted Sobolev spaces.

Show me the PDF file (349 KB), TEX file, and other files for this article.

Eddye Bustamante M.
Departamento de Matemáticas
Universidad Nacional de Colombia
A. A. 3840 Medellín, Colombia
email: eabusta0@unal.edu.co
José Jiménez U.
Departamento de Matemáticas
Universidad Nacional de Colombia
A. A. 3840 Medellín, Colombia
email: jmjimene@unal.edu.co
Jorge Mejía L.
Departamento de Matemáticas
Universidad Nacional de Colombia
A. A. 3840 Medellín, Colombia
email: jemejia@unal.edu.co

Return to the EJDE web page