Free boundary value problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
Free boundary value problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
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DOI：
10.1080/00036811.2013.852662
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发表时间：
2014-07
影响因子：
1.1
通讯作者：
Ruxu Lian;Zigao Chen
中科院分区：
文献类型：
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作者：
Ruxu Lian;Zigao Chen
本文研究了具有密度依赖粘性系数的一维等熵可压缩Navier-Stokes方程的自由边值问题。在对初始数据作一定的假设下，我们证明了存在唯一的整体强解，分离流态和真空态的界面沿粒子路径沿着传播并以代数时间速率向外扩展，流密度在有限时间内严格为正，当时间趋于无穷大时也以代数时间速率逐点衰减到零.
We study the free boundary value problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. Under certain assumptions imposed on the initial data, we show that there exists a unique global strong solution, the interface separating the flow and vacuum state propagates along particle path and expands outwards at an algebraic time-rate, the flow density is strictly positive from blow for any finite time and decays pointwise to zero also at an algebraic time-rate as the time tends to infinity.