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

Debdeep Bhattacharya; Luiz Gustavo Farah; Svetlana Roudenko

doi:10.1016/j.jde.2019.11.092

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

Analysis of PDEs 2021-08-26 v1

Authors: 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].

Keywords

modified Zakharov-Kuznetsov equation global well-posedness low regularity data I-method ground state solution

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@article{arxiv.1906.05822,
  title  = {Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation},
  author = {Debdeep Bhattacharya and Luiz Gustavo Farah and Svetlana Roudenko},
  journal= {arXiv preprint arXiv:1906.05822},
  year   = {2021}
}

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29 pages

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

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