On the radius of spatial analyticity for the modified Kawahara equation on the line

Autor(es)

Petronilho, Gerson ^[1] ; da Silva, Priscila Leal ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Mathematische Nachrichten; v. 292, n. 9, p. 2032-2047, SEP 2019.
• Citações Web of Science: 0

Resumo

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well-posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data u0(x) that can be extended as holomorphic functions in a strip around the x-axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity r(t) given by r(t)>= ct-(4+delta), where delta>0 can be taken arbitrarily small and c is a positive constant. (AU)

• Processo FAPESP: 12/03168-7 - Teoria geométrica de EDP e várias variáveis complexas
• Beneficiário: Jorge Guillermo Hounie
• Modalidade de apoio: Auxílio à Pesquisa - Temático