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Mat. Zametki, 2015, Volume 97, Issue 1, Pages 13–22 (Mi mz10469)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Regularity of Solutions of the Cauchy Problem for the Zakharov–Kuznetsov Equation in Hölder Norms

A. P. Antonova, A. V. Faminskii

Peoples Friendship University of Russia, Moscow

Abstract: The problem of the interior regularity of generalized solutions of the Cauchy problem for the Zakharov–Kuznetsov equation is studied. The existence of Hölder-continuous derivatives of given solutions is established. The study is based on the properties of the fundamental solution of the corresponding linearized equation.

Keywords: Zakharov–Kuznetsov equation, Cauchy problem, interior regularity of a solution, Korteweg–de Vries equation.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 333
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 333).


DOI: https://doi.org/10.4213/mzm10469

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English version:
Mathematical Notes, 2015, 97:1, 12–20

Bibliographic databases:

Document Type: Article
UDC: 517.958
Received: 04.12.2013

Citation: A. P. Antonova, A. V. Faminskii, “On the Regularity of Solutions of the Cauchy Problem for the Zakharov–Kuznetsov Equation in Hölder Norms”, Mat. Zametki, 97:1 (2015), 13–22; Math. Notes, 97:1 (2015), 12–20

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Antonova, A. V. Faminskii, “On regularity of solutions for initial-boundary value problems for the Zakharov–Kuznetsov equation”, Journal of Mathematical Sciences, 233:4 (2018), 427–445  mathnet  crossref
    2. Hendy A.S., Macias-Diaz J.E., “a Numerically Efficient and Conservative Model For a Riesz Space-Fractional Klein-Gordon-Zakharov System”, Commun. Nonlinear Sci. Numer. Simul., 71 (2019), 22–37  crossref  isi
  • Математические заметки Mathematical Notes
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