Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces
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 weight...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2010-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/169/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |