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The Cauchy problem for the non-isentropic compressible MHD fluids: optimal time-decay rates
  • Wenting Huang,
  • Shengbin Fu
Wenting Huang
Beijing Normal University

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Shengbin Fu
Fuzhou University
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This paper is concerned with the time-decay rates of the strong solutions of the three dimensional non-isentropic compressible magnetohydrodynamic (MHD) system. First, motivated by Pu–Guo’s result [Z. Angew. Math. Phys. 64 (2013) 519–538], we establish the existence result of a unique local-in-time strong solution for the MHD system. Then, we derive a priori estimates and use the continuity argument to obtain the global-in-time solution, where the initial data should be bounded in L1-norm and is small in H2-norm. Finally, based on Fourier theory and the idea of cancellation of a low-medium frequent part as in [Sci. China Math. 65 (2022) 1199–1228], we get the optimal time-decay rates (including highest-order derivatives) of strong solutions for non-isentropic MHD fluids. Our result is the first one concerning with the optimal decay estimates of the highest-order derivatives of the non-isentropic MHD system.
19 Jul 2022Submitted to Mathematical Methods in the Applied Sciences
20 Jul 2022Submission Checks Completed
20 Jul 2022Assigned to Editor
28 Jul 2022Reviewer(s) Assigned
06 Nov 2022Review(s) Completed, Editorial Evaluation Pending
15 Nov 2022Editorial Decision: Revise Minor
16 Nov 20221st Revision Received
16 Nov 2022Submission Checks Completed
16 Nov 2022Assigned to Editor
16 Nov 2022Review(s) Completed, Editorial Evaluation Pending
29 Nov 2022Reviewer(s) Assigned
11 Jan 2023Editorial Decision: Accept