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Anisotropic Gevrey regularity for mKdV on the circle

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  • 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$\sigma$.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35B65.


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