The Fourier restriction norm method for the Zakharov-Kuznetsov equation

Axel Grünrock; Sebastian Herr

doi:10.3934/dcds.2014.34.2061

Article Contents

2014, Volume 34, Issue 5: 2061-2068. Doi: 10.3934/dcds.2014.34.2061

This issue Previous Article Dirichlet $(p,q)$-equations at resonance Next Article A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion

The Fourier restriction norm method for the Zakharov-Kuznetsov equation

Axel Grünrock^1, and
Sebastian Herr^2,

1.
Heinrich-Heine-Universität Düsseldorf, Mathematisches Institut, Universitätsstraße 1, 40225 Düsseldorf
2.
Universität Bielefeld, Fakultät für Mathematik, Postfach 10 01 31, 33501 Bielefeld

Received: February 2013

Revised: June 2013

Published: May 2014

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Abstract

The Cauchy problem for the Zakharov-Kuznetsov equation is shown to be locally well-posed in $H^s(\mathbb{R}^2)$ for all $s>\frac{1}{2}$ by using the Fourier restriction norm method and bilinear refinements of Strichartz type inequalities.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 42B37.

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References

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