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Well-posedness for the two-dimensional modified Zakharov-Kuznetsov equation. (English) Zbl 1197.35242
Summary: We prove that the initial value problem for the two-dimensional modified Zakharov-Kuznetsov equation is locally well-posed for data in H s ( 2 ), s>3/4. Even though the critical space for this equation is L 2 ( 2 ), we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35B65Smoothness and regularity of solutions of PDE
35Q60PDEs in connection with optics and electromagnetic theory
35A01Existence problems for PDE: global existence, local existence, non-existence
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness