@article{3da79484b3f24cd9a9684b8cd062dc3d,
title = "Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation",
abstract = "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 δ ∈ (3/2, ∞) for t > 0.",
keywords = "Analytic semigroup, Gevrey class, Korteweg-de Vries equation, Resolvent estimation",
author = "Jixun Chu and Coron, {Jean Michel} and Peipei Shang and Tang, {Shu Xia}",
note = "Funding Information: Manuscript received May 5, 2017. Revised July 2, 2017. 1Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China. E-mail: chujixun@126.com 2Sorbonne Universit{\'e}s, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 4 place Jussieu, F-75252 Paris, France; ETH Institut f{\"u}r Theoretische Studien (ETH-ITS), Clausiusstrasse 47, 8092 Z{\"u}rich, Switzerland. E-mail: coron@ann.jussieu.fr 3Corresponding author. School of Mathematical Sciences, Tongji University, Shanghai 200092, China; Sorbonne Universit{\'e}s, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 4 Place Jussieu, F-75252 Paris, France; EHT Institute for Mathematical Research (ETH-FIM), R{\"a}mistrasse 101, 8092 Z{\"u}rich, Switzerland. E-mail: peipeishang@hotmail.com 4Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada; Sorbonne Universit{\'e}s, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 4 Place Jussieu, F-75252 Paris, France. E-mail: shuxiatang.control@gmail.com ∗This work was supported by the National Natural Science Foundation of China (Nos. 11401021, 11471044, 11771336, 11571257), the LIASFMA, the ANR project Finite4SoS (No. ANR 15-CE23-0007) and the Doctoral Program of Higher Education of China (Nos. 20130006120011, 20130072120008). Publisher Copyright: {\textcopyright} 2018, Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2018",
month = mar,
day = "1",
doi = "10.1007/s11401-018-1060-x",
language = "English",
volume = "39",
pages = "201--212",
journal = "Chinese Annals of Mathematics. Series B",
issn = "0252-9599",
number = "2",
}