Singular support of the global attractor for a damped BBM equation

Jianhua Huang; Yanbin Tang; Ming Wang

doi:10.3934/dcdsb.2020345

Article Contents

2021, Volume 26, Issue 10: 5321-5335. Doi: 10.3934/dcdsb.2020345

This issue Previous Article Codimension one and two bifurcations in Cattaneo-Christov heat flux model Next Article Qualitative analysis of a generalized Nosé-Hoover oscillator

Singular support of the global attractor for a damped BBM equation

a.
College of Science, National University of Defense Technology, Changsha, 410073, China
b.
TAG_SUPSchool of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
c.
School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

^* Corresponding author: Ming Wang
^* Corresponding author: Ming Wang

Received: May 31, 2020

Early access: November 2020

Published: October 2021

The research was supported in part by the National Natural Science Foundations of China (Grant Nos. 11701535, 11771449 and 11471129), China Postdoctoral Science Foundation No. 2019T120966, the Fundamental Research Funds for the Central Universities, China University of Geosciences(Wuhan)(No. CUGSX01), and the Natural Science Foundation of Hunan Province No. 2020JJ4102

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Abstract

The singular support of the global attractor is introduced. It is shown that the singular support of the global attractor for a damped BBM equation equals to the singular support of the force term. This gives a delicate description of the local regularity, which roughly says that the attractor is smooth exactly where the force is smooth.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 37L30.

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