SMOOTHING PROPERTIES FOR A COUPLED ZAKHAROV-KUZNETSOV SYSTEM

Julie L. Levandosky; Octavio Vera

doi:10.58997/ejde.2023.11

SMOOTHING PROPERTIES FOR A COUPLED ZAKHAROV-KUZNETSOV SYSTEM

Julie L. Levandosky
, Octavio Vera

Departamento de Matemática

Framingham State University

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

Resumen

In this article we study the smoothness properties of solutions to a two-dimensional coupled Zakharov-Kuznetsov system. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u₀, v₀) possesses certain regularity and sufficient decay as x → ∞, then the solution (u(t), v(t)) will be smoother than (u₀, v₀) for 0 < t ≤ T where T is the existence time of the solution.

Idioma original	Inglés
Número de artículo	11
Publicación	Electronic Journal of Differential Equations
Volumen	2023
DOI	https://doi.org/10.58997/ejde.2023.11
Estado	Publicada - 2023

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title = "SMOOTHING PROPERTIES FOR A COUPLED ZAKHAROV-KUZNETSOV SYSTEM",

abstract = "In this article we study the smoothness properties of solutions to a two-dimensional coupled Zakharov-Kuznetsov system. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u0, v0) possesses certain regularity and sufficient decay as x → ∞, then the solution (u(t), v(t)) will be smoother than (u0, v0) for 0 < t ≤ T where T is the existence time of the solution.",

keywords = "Coupled Zakharov-Kuznetsov system, gain in regularity, weighted Sobolev space",

author = "Levandosky, \{Julie L.\} and Octavio Vera",

note = "Publisher Copyright: {\textcopyright} 2023, Texas State University - San Marcos.",

year = "2023",

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N2 - In this article we study the smoothness properties of solutions to a two-dimensional coupled Zakharov-Kuznetsov system. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u0, v0) possesses certain regularity and sufficient decay as x → ∞, then the solution (u(t), v(t)) will be smoother than (u0, v0) for 0 < t ≤ T where T is the existence time of the solution.

AB - In this article we study the smoothness properties of solutions to a two-dimensional coupled Zakharov-Kuznetsov system. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u0, v0) possesses certain regularity and sufficient decay as x → ∞, then the solution (u(t), v(t)) will be smoother than (u0, v0) for 0 < t ≤ T where T is the existence time of the solution.

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KW - gain in regularity

KW - weighted Sobolev space

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JO - Electronic Journal of Differential Equations

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SMOOTHING PROPERTIES FOR A COUPLED ZAKHAROV-KUZNETSOV SYSTEM

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