Gain of regularity for the KP-I equation

Julie Levandosky; Mauricio Sepúlveda; Octavio Vera Villagrán

doi:10.1016/j.jde.2008.01.016

Gain of regularity for the KP-I equation

Julie Levandosky
, Mauricio Sepúlveda
, Octavio Vera Villagrán

Mathematics Department
Framingham State University
Departamento de Ingeniería Matemática
Universidad de Concepción
Universidad del Bío-Bío

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 φ{symbol} possesses certain regularity and sufficient decay as x → ∞, then the solution u (t) will be smoother than φ{symbol} for 0 < t ≤ T where T is the existence time of the solution.

Original language	English
Pages (from-to)	762-808
Number of pages	47
Journal	Journal of Differential Equations
Volume	245
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2008.01.016
State	Published - 1 Aug 2008
Externally published	Yes

Keywords

Gain in regularity
KP-I equation
Weighted Sobolev space

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10.1016/j.jde.2008.01.016

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title = "Gain of regularity for the KP-I equation",

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 φ\{symbol\} possesses certain regularity and sufficient decay as x → ∞, then the solution u (t) will be smoother than φ\{symbol\} for 0 < t ≤ T where T is the existence time of the solution.",

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AU - Vera Villagrán, Octavio

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N2 - 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 φ{symbol} possesses certain regularity and sufficient decay as x → ∞, then the solution u (t) will be smoother than φ{symbol} for 0 < t ≤ T where T is the existence time of the solution.

AB - 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 φ{symbol} possesses certain regularity and sufficient decay as x → ∞, then the solution u (t) will be smoother than φ{symbol} for 0 < t ≤ T where T is the existence time of the solution.

KW - Gain in regularity

KW - KP-I equation

KW - Weighted Sobolev space

UR - https://www.scopus.com/pages/publications/44149122828

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DO - 10.1016/j.jde.2008.01.016

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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ER -

Gain of regularity for the KP-I equation

Abstract

Keywords

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