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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

8 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	762-808
Número de páginas	47
Publicación	Journal of Differential Equations
Volumen	245
N.º	3
DOI	https://doi.org/10.1016/j.jde.2008.01.016
Estado	Publicada - 1 ago 2008
Publicado de forma externa	Sí

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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.",

keywords = "Gain in regularity, KP-I equation, Weighted Sobolev space",

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AU - Vera Villagrán, Octavio

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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.

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KW - KP-I equation

KW - Weighted Sobolev space

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Gain of regularity for the KP-I equation

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