Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 3

Asymptotic behavior of short trajectories to nonhomogeneous heat-conducting magnetohydrodynamic equations

Pages: 207 – 224

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n3.a3

Authors

Pigong Han (Academy of Mathematics and Systems Science, C.A.S., Beijing, China; and School of Mathematical Sciences, University of C.A.S., Beijing, China)

Keke Lei (Academy of Mathematics and Systems Science, C.A.S., Beijing, China; and School of Mathematical Sciences, University of C.A.S., Beijing, China)

Chenggang Liu (School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, China)

Xuewen Wang (Academy of Mathematics and Systems Science, C.A.S., Beijing, China; and School of Mathematical Sciences, University of C.A.S., Beijing, China)

Abstract

In this paper, we study the asymptotic behavior of short trajectories of weak solutions to the 2D nonhomogeneous heat-conducting magnetohydrodynamic equations. Several bounds for short trajectories are obtained. An attracting set is constructed, which consists of orbits on [0, 1] of complete bounded solutions. Furthermore, the attracting set is compact in different topologies.

Keywords

incompressible heat-conducting flows, asymptotic behavior, nonhomogeneous, short trajectories

2010 Mathematics Subject Classification

Primary 35Q35. Secondary 35B40, 76W05.

Full Text (PDF format)

Xuewen Wang is the corresponding author.

This work is supported by the National Key R&D Program of China (Grant No. 2021YFA1000800); by the National Natural Science Foundation of China under Grant No. 11871457; and by the K. C. Wong Education Foundation, Chinese Academy of Sciences.

Received 3 December 2021

Published 23 May 2022