Time decay rate of solutions to the hyperbolic mhd equations in

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• 作者：Bei LI ^{Lbbeili2015@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hongjin ZHU ^{zhuhongjinZHJ@163.com" class="auth_mail" title="E-mail the corresponding author} ; Caidi ZHAO ; ^{zhaocaidi2013@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：hyperbolic MHD equations ; weak solution ; time decay rate
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：36
• 期：5
• 页码：1369-1382
• 全文大小：380 K

文摘

In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics (MHD) equations inℝ³${ℝ}^3$. Then we establish that the solutions with initial data belonging toHm(ℝ³)∩L¹(ℝ³)${\mathbb{H}}^{\text{m}}\left({ℝ}^3\right)\cap {\mathbb{L}}^1\left({ℝ}^3\right)$ have the following time decay rate:‖m^∇u(x,t)‖²+‖m^∇b(x,t)‖²+‖^∇m+1u(x,t)‖²+‖^∇m+1b(x,t)‖²≤c(1+t)^-3/2-m${\Vert {\nabla }^{m}u\left(x,t\right)\Vert }^2+{\Vert {\nabla }^{m}b\left(x,t\right)\Vert }^2+{\Vert {\nabla }^{m+1}u\left(x,t\right)\Vert }^2+{\Vert {\nabla }^{m+1}b\left(x,t\right)\Vert }^2\le c{\left(1+t\right)}^{-3/2-m}$ for large t, where m = 0, 1.