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On the periodic Zakharov-Kuznetsov equation

2019
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Discrete and Continuous Dynamical Systems. Series A
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We consider the Cauchy problem associated with the Zakharov-Kuznetsov equation, posed on T 2 . We prove the local well-posedness for given data in H s (T 2 ) 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 R 2 and R × T settings. Our interest here is in studying the local well-posedness issue to the IVP (1) for given data in the periodic Sobolev

doi:10.3934/dcds.2019145
fatcat:nptwuf7denbzrkv4wkncnfqw3y