Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D

Kinoshita S (2021)
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 38(2): 451-505.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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 H-s(R-2) 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 L-2(R-2). (C) 2020 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.
Stichworte
Well-posedness; Cauchy problem; Low regularity; Bilinear estimate; Nonlinear Loomis-Whitney inequality
Erscheinungsjahr
2021
Zeitschriftentitel
Annales de l'Institut Henri Poincaré C, Analyse non linéaire
Band
38
Ausgabe
2
Seite(n)
451-505
ISSN
0294-1449
eISSN
1873-1430
Page URI
https://pub.uni-bielefeld.de/record/2952717

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Kinoshita S. Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 2021;38(2):451-505.
Kinoshita, S. (2021). Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 38(2), 451-505. https://doi.org/10.1016/j.anihpc.2020.08.003
Kinoshita, S. (2021). Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 38, 451-505.
Kinoshita, S., 2021. Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 38(2), p 451-505.
S. Kinoshita, “Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D”, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, vol. 38, 2021, pp. 451-505.
Kinoshita, S.: Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D. Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 38, 451-505 (2021).
Kinoshita, Shinya. “Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D”. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 38.2 (2021): 451-505.

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