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Gain of regularity for the KP-I equation |
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| Authors: | Julie Levandosky,Mauricio Sepú lveda |
| Affiliation: | a Mathematics Department, Framingham State College, Framingham, MA 01701, USA b CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile c Departamento de Matemática, Universidad del Bío-Bío Collao 1202, Casilla 5-C, Concepción, Chile |
| Abstract: | In this paper we study the smoothness properties of solutions to the KP-I equation. We show that the equation's dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data ? possesses certain regularity and sufficient decay as x→∞, then the solution u(t) will be smoother than ? for 0<t?T where T is the existence time of the solution. |
| Keywords: | KP-I equation Gain in regularity Weighted Sobolev space |
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