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2011, 2011(Special): 634-642. doi: 10.3934/proc.2011.2011.634

Anisotropic Gevrey regularity for mKdV on the circle

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

Received  July 2010 Revised  April 2011 Published  October 2011

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$\sigma$.
Citation: Heather Hannah, A. Alexandrou Himonas, Gerson Petronilho. Anisotropic Gevrey regularity for mKdV on the circle. Conference Publications, 2011, 2011 (Special) : 634-642. doi: 10.3934/proc.2011.2011.634
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