A remark on regularity of 1D compressible isentropic Navier–Stokes equations with density-dependent viscosity
A remark on regularity of 1D compressible isentropic Navier–Stokes equations with density-dependent viscosity
复制标题
密度依赖粘度的一维可压缩等熵纳维-斯托克斯方程的正则性评述
DOI：
10.1016/j.jmaa.2008.10.044
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发表时间：
2009
影响因子：
1.3
通讯作者：
["Yuming Qin
中科院分区：
文献类型：
--
作者：
["Yuming Qin
本文考虑具有黏度随密度变化和自由边界的一维可压缩等熵Navier-Stokes方程。粘度系数μ与ρθ与θ>0成正比，其中ρ为密度。Xin和Yao在[Z]中证明了H1（[0,1]）全局弱解的存在性、唯一性和正则性。姚志刚，姚志刚，一维可压缩Navier-Stokes方程的存在性、唯一性和正则性，预印本[j]。此外，在对初始数据施加一定假设的情况下，我们改进了[Z]中得到的正则性结果。姚志刚，姚志刚，基于先验估计的一维可压缩Navier-Stokes方程的存在性、唯一性和正则性[j]。
In this paper, we consider one-dimensional compressible isentropic Navier–Stokes equations with the viscosity depending on density and with the free boundary. The viscosity coefficient μ is proportional to ρθwith θ>0, where ρ is the density. The existence, uniqueness, regularity of global weak solutions in H1([0,1]) have been established by Xin and Yao in [Z. Xin, Z. Yao, The existence, uniqueness and regularity for one-dimensional compressible Navier–Stokes equations, preprint]. Furthermore, under certain assumptions imposed on the initial data, we improve the regularity result obtained in [Z. Xin, Z. Yao, The existence, uniqueness and regularity for one-dimensional compressible Navier–Stokes equations, preprint] by driving some new a priori estimates.