Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation

Linares, F.; Pastor, A.; Drumond Silva, J.

doi:10.1016/j.anihpc.2020.07.002

Linares, F.¹ ; Pastor, A.² ; Drumond Silva, J.³

¹ a IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, RJ, Brazil
² b IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas-SP, Brazil
³ c Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 281-300.

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Résumé

The main purpose here is the study of dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Dispersive blow-up refers to point singularities due to the focusing of short or long waves. We will construct initial data such that solutions of the linear problem present this kind of singularities. Then we show that the corresponding solutions of the nonlinear problem present dispersive blow-up inherited from the linear component part of the equation. Similar results are obtained for the generalized Zakharov-Kuznetsov equation.

DOI : 10.1016/j.anihpc.2020.07.002

Classification : 35Q53, 35B44
Mots-clés : Nonlinear dispersive equations, Zakharov-Kuznetsov equation, Dispersive blow-up

Affiliations des auteurs :

Linares, F. ¹ ; Pastor, A. ² ; Drumond Silva, J. ³

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     title = {Dispersive blow-up for solutions of the {Zakharov-Kuznetsov} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {281--300},
     publisher = {Elsevier},
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Linares, F.; Pastor, A.; Drumond Silva, J. Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation. Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 281-300. doi : 10.1016/j.anihpc.2020.07.002. http://www.numdam.org/articles/10.1016/j.anihpc.2020.07.002/

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