Electron. J. Differential Equations, Vol. 2023 (2023), No. 11, pp. 1-41.

Smoothing properties for a coupled Zakharov-Kuznetsov system

Julie L. Levandosky, Octavio Vera

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.

Submitted April 18, 2022. Published February 4, 2023.
Math Subject Classifications: 35Q53, 35Q35, 47J35.
Key Words: Coupled Zakharov-Kuznetsov system; gain in regularity; weighted Sobolev space.
DOI: https://doi.org/10.58997/ejde.2023.11

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Julie L. Levandosky
Department of Mathematics
Framingham State University
Framingham, MA 01701 USA
email: jlevandosky@framingham.edu
  Octavio Vera
Departamento de Matemáticas
Universidad de Tarapaca
Casilla 7-D, Arica, Chile
email: opverav@academicos.uta.cl

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