Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces

Electronic Journal of Differential Equations

卷:2010

关键词: Schrodinger equation;    Korteweg-de Vries equation;    global well-posed;    persistence property;    weighted Sobolev spaces;   

DOI  :  

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown