Methods and Applications of Analysis

Volume 29 (2022)

Number 1

Special issue dedicated to Professor Ling Hsiao on the occasion of her 80th birthday, Part IV

Guest editors: Qiangchang Ju (Institute of Applied Physics and Computational Mathematics, Beijing), Hailiang Li (Capital Normal University, Beijing), Tao Luo (City University of Hong Kong), and Zhouping Xin (Chinese University of Hong Kong)

Global well-posedness and large time behavior to 2D Boussinesq equations for MHD convection

Pages: 31 – 56



Shasha Wang (Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, Hebei, China )

Wen-Qing Xu (Department of Mathematics and Statistics, California State University, Long Beach, Calif., U.S.A.)

Jitao Liu (Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, China)


We study the Cauchy problem for the 2D incompressible MHD-Boussinesq equations without thermal diffusion. We prove the global existence and uniqueness of the solutions for suitably regular initial data. To obtain large time decay properties of the solutions, we insert an artificial thermal damping term. By applying the classical Fourier splitting methods, we derive optimal large time decay rates of the solutions and their first-order derivatives.


MHD-Boussinesq equations, global well-posedness, large time behavior, Fourier splitting

2010 Mathematics Subject Classification

35B40, 35Q35, 76D03

J. Liu is supported by the National Natural Science Foundation of China (No. 11801018), Beijing Natural Science Foundation (No. 1192001), and by the Beijing University of Technology (No. 006000514122514).

Received 7 September 2020

Accepted 13 January 2021

Published 10 June 2022