Electron. J. Diff. Equ., Vol. 2010(2010), No. 169, pp. 1-10.

Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces

Xavier Carvajal Paredes, Pedro Gamboa Romero

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.

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Xavier Carvajal
IM UFRJ, Av. Athos da Silveira Ramos
P.O. Box 68530. CEP 21945-970. RJ. Brazil
email: carvajal@im.ufrj.br, Phone 55-21-25627520
Pedro Gamboa Romero
IM UFRJ, Av. Athos da Silveira Ramos
P.O. Box 68530. CEP 21945-970. RJ. Brazil
email: pgamboa@im.ufrj.br, Phone 55-21-25627520

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