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arXiv · 1906.05822

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

Debdeep Bhattacharya·Luiz Gustavo Farah·Svetlana Roudenko
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Abstract

We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$-method, we prove the global well-posedness of the $H^s$ solutions for $s>\frac{3}{4}$ for any data in the defocusing case and under the assumption that the mass of the initial data is less than the mass of the ground state solution of $\Delta \varphi - \varphi + \varphi^3 = 0$ in the focusing case. This improves the global well-posedness result of Linares and Pastor [20].

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Debdeep Bhattacharya, Luiz Gustavo Farah, Svetlana Roudenko. 2019-06-13. Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation. https://doi.org/10.1016/j.jde.2019.11.092

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