ON THE PERIODIC ZAKHAROV-KUZNETSOV EQUATION

Linares, Felipe; Panthee, Mahendra; Robert, Tristan; Tzvetkov, Nikolay

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON THE PERIODIC ZAKHAROV-KUZNETSOV EQUATION

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Author(s):	Linares, Felipe ^[1] ; Panthee, Mahendra ^[2] ; Robert, Tristan ^[3] ; Tzvetkov, Nikolay ^[3] Total Authors: 4
Affiliation:	^[1] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro - Brazil ^[2] IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil ^[3] Univ Cergy Pontoise, UMR 8088, CNRS, F-95000 Cergy Pontoise - France Total Affiliations: 3
Document type:	Journal article
Source:	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 39, n. 6, p. 3521-3533, JUN 2019.
Web of Science Citations:	0
Abstract
We consider the Cauchy problem associated with the Zakharov-Kuznetsov equation, posed on T-2. We prove the local well-posedness for given data in H-8(T-2) whenever s > 5/3. More importantly, we prove that this equation is of quasi-linear type for initial data in any Sobolev space on the torus, in sharp contrast with its semi-linear character in the R-2 and R x T settings. (AU)

FAPESP's process:	16/25864-6 - Nonlinear Evolution Equations of Dispersive Type
Grantee:	Mahendra Prasad Panthee
Support Opportunities:	Regular Research Grants

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