Anisotropic Gevrey regularity for mKdV on the circle

Pages: 634 - 642, Issue Special, September 2011

 Abstract        Full Text (348.7K)              

Heather Hannah - Department of Mathematics, East Central University, Ada, OK 74820, United States (email)
A. Alexandrou Himonas - Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United States (email)
Gerson Petronilho - Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP 13565-905, Brazil (email)

Abstract: It is shown that the solution to the Cauchy problem for the modifi ed 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:  Modi ed KdV equation, mKdV, Cauchy problem, periodic, Gevrey regularity, Sobolev spaces
Mathematics Subject Classification:  Primary: 35Q53; Secondary: 35B65

Received: July 2010;      Revised: April 2011;      Published: October 2011.