论文标题
全球适合三维完全可压缩的磁性水力动力方程的适合度
Global well-posedness to three-dimensional full compressible magnetohydrodynamic equations with vacuum
论文作者
论文摘要
本文研究了三维粘性，可压缩和热传导磁流体动力学方程的库奇问题。我们证明了强大解决方案的全球存在和独特性，但规定数量$ \ |ρ_0\ | _ {l^\ infty}+\ | b_0 \ | _ {l^3} $很小，粘度系数满足$3μ>λ$。在这里，初始速度和初始温度可能很大。对初始密度的假设并不排除在$ \ mathbb {r}^3 $的子集中消失的初始密度，并且可以是非平整的紧凑支持。我们的结果是Fan和Yu \ cite {fy09}和Li等人的作品的扩展。 \ cite {lxz13}，其中分别获得了三个维度的局部强解决方案和等屈态情况的全局强溶液。该分析基于一些新的数学技术和一些新的有用能量估计。本文可以看作是关于在较高维度的某些大数据中，无穷大的真空存在强大解决方案的首个结果。
This paper studies the Cauchy problem for three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic equations with vacuum as far field density. We prove the global existence and uniqueness of strong solutions provided that the quantity $\|ρ_0\|_{L^\infty}+\|b_0\|_{L^3}$ is suitably small and the viscosity coefficients satisfy $3μ>λ$. Here, the initial velocity and initial temperature could be large. The assumption on the initial density do not exclude that the initial density may vanish in a subset of $\mathbb{R}^3$ and that it can be of a nontrivially compact support. Our result is an extension of the works of Fan and Yu \cite{FY09} and Li et al. \cite{LXZ13}, where the local strong solutions in three dimensions and the global strong solutions for isentropic case were obtained, respectively. The analysis is based on some new mathematical techniques and some new useful energy estimates. This paper can be viewed as the first result concerning the global existence of strong solutions with vacuum at infinity in some classes of large data in higher dimension.
