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

Author(s)

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

Affiliation

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

• Document type: Journal article
• Source: Mathematische Nachrichten; v. 292, n. 9, p. 2032-2047, SEP 2019.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
• Grantee: Jorge Guillermo Hounie
• Support Opportunities: Research Projects - Thematic Grants