Linares, Felipe; Pastor, Ademir Well-posedness for the two-dimensional modified Zakharov-Kuznetsov equation. (English) Zbl 1197.35242 SIAM J. Math. Anal. 41, No. 4, 1323-1339 (2009). Summary: We prove that the initial value problem for the two-dimensional modified Zakharov-Kuznetsov equation is locally well-posed for data in \(H^s(\mathbb R^2)\), \(s>3/4\). Even though the critical space for this equation is \(L^2(\mathbb R^2)\), we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established. Cited in 76 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35B65 Smoothness and regularity of solutions to PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness Keywords:well-posedness; ill-posedness; maximal function; Zakharov-Kuznetsov equation PDFBibTeX XMLCite \textit{F. Linares} and \textit{A. Pastor}, SIAM J. Math. Anal. 41, No. 4, 1323--1339 (2009; Zbl 1197.35242) Full Text: DOI