On the periodic Zakharov-Kuznetsov equation

2018/09/06 by Linares, Felipe, Panthee, Mahendra, Robert, Tristan +1 · 1 citation
#35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.02027

Abstract

We consider the Cauchy problem associated with the Zakharov-Kuznetsov equation, posed on \mathbbT². We prove the local well-posedness for given data in H^s(\mathbbT²) whenever s>5/3. More importantly, we prove that this equation is of quasi-linear type for initial data in any Sobolev space on the torus, in sharp contrast with its semi-linear character in the ℝ² and ℝ× \mathbbT settings.

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• Long-Time Dynamics of the Zakharov-Kuznetsov Equation

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