Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 169, pp. 1-10.
Title: Persistence of solutions to nonlinear evolution equations in
weighted Sobolev spaces
Authors: Xavier Carvajal Paredes (IM UFRJ, Brazil)
Pedro Gamboa Romero (IM UFRJ, Brazil)
Abstract:
In this article, we prove that the initial value problem associated with
the Korteweg-de Vries equation is well-posed in weighted
Sobolev spaces $\mathcal{X}^{s,\theta}$,
for $s \geq 2\theta \ge 2$ and the initial value problem
associated with the nonlinear Schrodinger equation is
well-posed in weighted Sobolev spaces $\mathcal{X}^{s,\theta}$,
for $s \geq \theta \geq 1$. Persistence property has been
proved by approximation of the solutions and using
a priori estimates.
Submitted October 18, 2010. Published November 24, 2010.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Schrodinger equation; Korteweg-de Vries equation;
global well-posed; persistence property; weighted Sobolev spaces.