Well-posedness for the Cauchy Problem of the Modified Zakharov-Kuznetsov Equation

Abstract

This paper is concerned with the Cauchy problem of the modified Zakharov-Kuznetsov equation on Rd. If d = 2, we prove the sharp estimate which implies local in time well-posedness in the Sobolev space Hs(R2) for s ≥ 1/4. If d ≥ 3, by employing Up and Vp spaces, we establish the small data global well-posedness in the scaling critical Sobolev space Hsc(Rd) where sc = d/2-1.

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