Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries equation

Chu Ji-Xun; Jean-Michel Coron; Shang Pei-Pei; Tang Shu-Xia

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Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries equation

Chu Ji-Xun 1 #,Jean-Michel Coron 2,Shang Pei-Pei 3 *,Tang Shu-Xia 4

1.School of Mathematics and Physics, University of Science andTechnology Beijing, Beijing 100083

2.Laboratoire Jacques-Louis Lions, Universit\'{e} Pierre et Marie Curie-Paris 6, Paris 75005

3.School of Mathematical Sciences, Tongji University, Shanghai 200092

4.Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1

*Correspondence author

#Submitted by

Subject:

Funding: National Natural Science Foundation of China（No.11401021, 11471044, 11301387, 11571257）, Doctoral Program of Higher Education（No.20130006120011, 20130072120008）

Opened online: 3 May 2017

Accepted by: none

Citation: Chu Ji-Xun,Jean-Michel Coron,Shang Pei-Pei.Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries equation[OL]. [ 3 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4728194

In this paper, the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV) equation is considered. By estimating the resolvent of the corresponding linear operator, it can be concluded that thesemigroup generated by the linear operator is not analytic but of Gevrey class $deltain(3/2,infty)$ for $t>0$.

Keywords:Applied Mathematics; Korteweg-de Vries equation; resolvent estimation; analytic semigroup; Gevrey class

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