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Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation

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arxiv 2003.02694 v1 pith:F5DYHZ3W submitted 2020-03-05 math.AP math.CA

Shinya Kinoshita , Robert Schippa This is my paper · ORCID
classification math.APmath.CA
keywords equationloomis-whitney-typeperiodicwell-posednesszakharov-kuznetsovcasecontroldata
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abstract

Local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in the fully periodic case with initial data in Sobolev spaces $H^s$, $s>1$, is proved. Frequency dependent time localization is utilized to control the derivative nonlinearity. The new ingredient to improve on previous results is a nonlinear Loomis-Whitney-type inequality.

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