ON THE PERIODIC ZAKHAROV-KUZNETSOV EQUATION

Autor(es)

Linares, Felipe ^[1] ; Panthee, Mahendra ^[2] ; Robert, Tristan ^[3] ; Tzvetkov, Nikolay ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 39, n. 6, p. 3521-3533, JUN 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/25864-6 - Equações de Evolução Nãolineares tipo Dispersivas
• Beneficiário: Mahendra Prasad Panthee
• Modalidade de apoio: Auxílio à Pesquisa - Regular