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The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time‐decay rates.
- Source :
-
Mathematical Methods in the Applied Sciences . 5/30/2023, Vol. 46 Issue 8, p9708-9735. 28p. - Publication Year :
- 2023
-
Abstract
- This paper is concerned with the time‐decay rates of the strong solutions of the three‐dimensional nonisentropic compressible magnetohydrodynamic (MHD) system. First, motivated by Pu and 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 perturbation is small in H2$$ {H}^2 $$‐norm. Finally, based on Fourier theory and the idea of cancelation 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 nonisentropic MHD fluids when the boundedness of L1$$ {L}^1 $$‐norm of the initial perturbation is required. Our result is the first one concerning with the optimal decay estimates of the highest‐order derivatives of the nonisentropic MHD system. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CAUCHY problem
*FLUIDS
*IDEA (Philosophy)
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 163604248
- Full Text :
- https://doi.org/10.1002/mma.9082