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.

41 pages

References in corpus (4)

• Global well-posedness of the KP-I initial-value problem in the energy space
• Convolutions of singular measures and applications to the Zakharov system
• On the 2d Zakharov system with L^2 Schrödinger data
• Disentanglement, Multilinear Duality and Factorisation for non-positive operators

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