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.

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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

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