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

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.

arXiv comment41 pages

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Cited by in corpus (2)

• Low regularity well-posedness for KP-I equations: the dispersion-generalized case
• Well-posedness and ill-posedness for a system of periodic quadratic derivative nonlinear Schrödinger equations