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

Petronilho, Gerson; da Silva, Priscila Leal

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

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Author(s):	Petronilho, Gerson ^[1] ; da Silva, Priscila Leal ^[1] Total Authors: 2
Affiliation:	^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil Total Affiliations: 1
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

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