Geodesic
Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
Kinoshita, Shinya1
1 Universität Bielefeld, Fakultät für Mathematik, Postfach 10 01 31, 33501, Bielefeld, Germany
Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 451-505

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This paper is concerned with the Cauchy problem of the 2D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness in the Sobolev space Hs(R2) for s>−1/4, and these are optimal up to the endpoint. We utilize the nonlinear version of the classical Loomis-Whitney inequality and develop an almost orthogonal decomposition of the set of resonant frequencies. As a corollary, we obtain global well-posedness in L2(R2).

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DOI : 10.1016/j.anihpc.2020.08.003
Classification : 35Q53, 35A01
Keywords: Well-posedness, Cauchy problem, Low regularity, Bilinear estimate, Nonlinear Loomis-Whitney inequality

Kinoshita, Shinya 1

1 Universität Bielefeld, Fakultät für Mathematik, Postfach 10 01 31, 33501, Bielefeld, Germany 
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     title = {Global well-posedness for the {Cauchy} problem of the {Zakharov-Kuznetsov} equation in {2D}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {451--505},
     publisher = {Elsevier},
     volume = {38},
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Kinoshita, Shinya. Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 451-505. doi: 10.1016/j.anihpc.2020.08.003

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