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Zbl 1197.35242
Linares, Felipe; Pastor, Ademir
Well-posedness for the two-dimensional modified Zakharov-Kuznetsov equation. (English)
[J] SIAM J. Math. Anal. 41, No. 4, 1323-1339 (2009). ISSN 0036-1410; ISSN 1095-7154/e

Summary: We prove that the initial value problem for the two-dimensional modified Zakharov-Kuznetsov equation is locally well-posed for data in $H^s(\Bbb R^2)$, $s>3/4$. Even though the critical space for this equation is $L^2(\Bbb R^2)$, we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established.

MSC 2000:: *35Q53 KdV-like equations
35B65 Smoothness of solutions of PDE
35Q60 PDE of electromagnetic theory and optics
35A01
35A02

Keywords: well-posedness; ill-posedness; maximal function; Zakharov-Kuznetsov equation

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