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Global regularity problem of two-dimensional magnetic B\’{e}nard fluid equations
  • Liangliang Ma
Liangliang Ma
Chengdu University of Technology
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Abstract

In the paper, we devote to broadening the current global regularity results for the two-dimensional magnetic B\’{e}nard fluid equations. We study three cases: (i) fractional Laplacian dissipation $(-\Delta)^\alpha{u}$, partial magnetic diffusion $(\partial_{x_2x_2}b_1,\partial_{x_1x_1}b_2)$ and Laplacian thermal diffusivity $\Delta\theta$; (ii) partial fractional dissipation $(\Lambda^{2\alpha}_{x_2}u_1,\Lambda^{2\alpha}_{x_1}u_2)$, partial magnetic diffusion $(\partial_{x_2x_2}b_1,\partial_{x_1x_1}b_2)$ and Laplacian thermal diffusivity $\Delta\theta$; (iii) partial fractional magnetic diffusion $(\Lambda^{2\beta}_{x_2}b_1,\Lambda^{2\beta}_{x_1}b_2)$, Laplacian thermal diffusivity $\Delta\theta$ and without Laplacian dissipation $\Delta{u}$ (i.e., $\mu=0$)), and establish the global regularity for each cases.

Peer review status:UNDER REVIEW

09 Jan 2020Submitted to Mathematical Methods in the Applied Sciences
03 Apr 2020Assigned to Editor
03 Apr 2020Submission Checks Completed
07 Apr 2020Reviewer(s) Assigned
23 Jul 2020Review(s) Completed, Editorial Evaluation Pending