Anisotropic Gevrey regularity for mKdV on the circle

Heather Hannah; A. Alexandrou Himonas; Gerson Petronilho

doi:10.3934/proc.2011.2011.634

Article Contents

2011, Volume 2011: 634-642. Doi: 10.3934/proc.2011.2011.634 open access

This issue Previous Article 3D-2D asymptotic observation for minimization problems associated with degenerate energy-coefficients Next Article Pohozaev-Ôtani type inequalities for weak solutions of quasilinear elliptic equations with homogeneous coefficients

Anisotropic Gevrey regularity for mKdV on the circle

1.
Department of Mathematics, East Central University, Ada, OK 74820
2.
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556
3.
Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP 13565-905

Received: June 30, 2010

Revised: March 31, 2011

Published: August 2017

Abstract Related Papers Cited by

Abstract

It is shown that the solution to the Cauchy problem for the modified Korteweg-de Vries equation with initial data in an analytic Gevrey space $G^\sigma$, $\sigma \>= 1$, as a function of the spacial variable belongs to the same Gevrey space. However, considered as function of time the solution does not belong to $G^\sigma$. In fact, it belong to $G^(3\sigma)$ and not to any Gevrey space $G^r$, 1 $\<= r$ < 3$\sigma$.

Keywords:

Mathematics Subject Classification: Primary: 35Q53; Secondary: 35B65.

Citation:

Article Metrics

HTML views() PDF downloads(71) Cited by(0)

Anisotropic Gevrey regularity for mKdV on the circle

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Anisotropic Gevrey regularity for mKdV on the circle

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content