Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces

• Main Authors: Xavier Carvajal Paredes, Pedro Gamboa Romero
• Format: Article
• Language: English
• Published: Texas State University 2010-11-01
• Series: Electronic Journal of Differential Equations
• Subjects: Schrodinger equation; Korteweg-de Vries equation; global well-posed; persistence property; weighted Sobolev spaces
• Online Access: http://ejde.math.txstate.edu/Volumes/2010/169/abstr.html

In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq 2heta ge 2$ and the initial value problem associated with the nonlinear Schrodinger equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq heta geq 1$. Persistence property has been proved by approximation of the solutions and using a priori estimates.