Compressible Navier–Stokes Equations with Degenerate Viscosity Coefficient and Vacuum
Compressible Navier–Stokes Equations with Degenerate Viscosity Coefficient and Vacuum
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DOI：
10.1007/s00220-002-0703-6
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发表时间：
2002-10
影响因子：
2.4
通讯作者：
Tong Yang;Changjiang Zhu
中科院分区：
文献类型：
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作者：
Tong Yang;Changjiang Zhu
本文考虑有限总质量等熵流的可压缩Navier-Stokes方程，当初始密度为紧支集或无限支集时。粘性系数被假定为密度的幂函数，使得柯西问题是适定的。当密度函数连续地与真空态相连时，建立了新的整体存在性结果。为此，得到了一些新的优先估计，以照顾在真空下的粘度系数的简并性。我们也将给出一个非整体的正则解的存在性定理时，初始数据是紧支持在欧拉坐标，这意味着奇异形式的界面分离的气体和真空。
In this paper, we consider the compressible Navier–Stokes equations for isentropic flow of finite total mass when the initial density is either of compact or infinite support. The viscosity coefficient is assumed to be a power function of the density so that the Cauchy problem is well-posed. New global existence results are established when the density function connects to the vacuum states continuously. For this, some newa prioriestimates are obtained to take care of the degeneracy of the viscosity coefficient at vacuum. We will also give a non-global existence theorem of regular solutions when the initial data are of compact support in Eulerian coordinates which implies singularity forms at the interface separating the gas and vacuum.