论文标题
大约3D可压缩MHD方程的大型大型时间衰减估计
Optimal time decay estimation for large-solution about 3D compressible MHD equations
论文作者
论文摘要
本文主要集中于3D整个空间中有关可压缩磁性流体动力方程的大型最佳时间衰减估计，但前提是$（σ_{0} -1，u_ {0}，m_ {0}，m_ {0}）\ in L^1 \ cap H^2 $。在[2]（Chen等，2019）中，他们证明了$ \ |（σ-1，U，m）\ | _ {h^1} $为$（1+t）^{ - \ frac {3} {4}} $的时间衰减估计。基于它，我们获得了$ \ | \ nabla（σ-1，u，m）\ | _ {h^1} $为$（1+t）^{ - \ frac {5} {4}}} $ [24]。因此，我们致力于改善本文中的$ \ | \ nabla^2（σ-1，u，m）\ | _ {l^2} $。得益于[25]中采用的方法（Wang and Wen，2021），我们获得了解决方案空间的最佳时间衰减估计，这意味着时间衰减的$ \ | \ | \ nabla^2（σ-1，U，U，U，M）\ | __________ {l^2} $（1+T）$（1+T）
This paper mainly focus on optimal time decay estimation for large-solution about compressible magnetohydrodynamic equations in 3D whole space, provided that $(σ_{0}-1,u_{0},M_{0})\in L^1\cap H^2$. In [2](Chen et al.,2019), they proved time decay estimation of $\|(σ-1,u,M)\|_{H^1}$ being $(1+t)^{-\frac{3}{4}}$. Based on it, we obtained that of $\|\nabla(σ-1,u,M)\|_{H^1}$ being $(1+t)^{-\frac{5}{4}}$ in [24]. Therefore, we are committed to improving that of $\|\nabla^2 (σ-1,u,M)\|_{L^2}$ 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 $\|\nabla^2 (σ-1,u,M)\|_{L^2}$ is $(1+t)^{-\frac{7}{4}}$.
