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Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries equation. (English) Zbl 1392.35258

Summary: In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class \(\delta\in (\frac{3}{2},\infty)\) for \(t>0\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35P05 General topics in linear spectral theory for PDEs
47D03 Groups and semigroups of linear operators
35B65 Smoothness and regularity of solutions to PDEs
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