Optimal time decay estimation for large-solution about 3D compressible MHD equations

2022/06/10 by Shuai Wang, Fei Chen, Wang, Shuai +3
Mathematics · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Meteorological Phenomena and Simulations

paper · pdf · doi:10.48550/arxiv.2206.05117

Abstract

This paper mainly focus on optimal time decay estimation for large-solution about compressible magnetohydrodynamic equations in 3D whole space, provided that (σ₀-1,u₀,M₀)∈ L¹∩ H². In [2](Chen et al.,2019), they proved time decay estimation of ‖(σ-1,u,M)‖_H¹ being (1+t)^-(3)/(4). Based on it, we obtained that of ‖∇(σ-1,u,M)‖_H¹ being (1+t)^-(5)/(4) in [24]. Therefore, we are committed to improving that of ‖∇² (σ-1,u,M)‖_L² in this paper. Thanks to the method adopted in [25] (Wang and Wen, 2021), we get the optimal time decay estimation to the highest-order derivative for space of solution, which means that time decay estimation of ‖∇² (σ-1,u,M)‖_L² is (1+t)^-(7)/(4).

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