Analytical solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients and free boundaries
Analytical solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients and free boundaries
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DOI：
10.1016/j.jde.2012.03.023
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发表时间：
2012-07
影响因子：
2.4
通讯作者：
Zhenhua Guo;Z. Xin
中科院分区：
文献类型：
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作者：
Zhenhua Guo;Z. Xin
本文研究了一类粘性系数依赖于密度的可压缩Navier-Stokes方程的解析解，该方程描述了可压缩流体向真空外运动的情形。对于适当的粘性多变流体，在RN（N ≠ 2）中构造了一类径向对称的自相似解析解，该解析解同时满足连续密度条件和无应力条件.这样的解决方案表现出有趣的新信息，如真空的对称中心的形成，时间趋于无穷大和明确的时间衰减估计的速度场。
In this paper, we study a class of analytical solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients, which describe compressible fluids moving into outer vacuum. For suitable viscous polytropic fluids, we construct a class of radial symmetric and self-similar analytical solutions in RN(N⩾2) with both continuous density condition and the stress free condition across the free boundaries separating the fluid from vacuum. Such solutions exhibit interesting new information such as the formation of vacuum at the center of the symmetry as time tends to infinity and explicit regularities and large time decay estimates of the velocity field.