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Gevrey regularity of the periodic gKdV equation. (English) Zbl 1209.35117
Summary: Using the multilinear estimates, which were derived for proving well-posedness of the generalized Korteweg-de Vries (gKdV) equation, it is shown that if the initial data belongs to Gevrey space \(G^{\sigma} , \sigma \geqslant 1\), in the space variable then the solution to the corresponding Cauchy problem for gKdV belongs also to \(G^{\sigma }\) in the space variable. Moreover, the solution is not necessarily \(G^{\sigma }\) in the time variable. However, it belongs to \(G^{3\sigma }\) near 0. When \(\sigma =1\) these are analytic regularity results for gKdV.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B65 Smoothness and regularity of solutions to PDEs
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