Zero Dissipation Limit to Rarefaction Wave with Vacuum for One-Dimensional Compressible Navier-Stokes Equations
Zero Dissipation Limit to Rarefaction Wave with Vacuum for One-Dimensional Compressible Navier-Stokes Equations
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DOI：
10.1137/100814305
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
F. Huang;Mingjie Li;Yi Wang
中科院分区：
文献类型：
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作者：
F. Huang;Mingjie Li;Yi Wang
众所周知，一维等熵气体动力学有两个基本波，即，冲击波和稀疏波。在这两种波中，只有稀疏波可以与真空相联系。对可压缩Euler方程组给出一个单侧真空状态的稀疏波，我们可以构造出一维可压缩等熵Navier-Stokes方程组的一系列解，当粘性趋于零时，这些解收敛于上述真空状态的稀疏波。此外，还得到了一致收敛速度。证明包括一个标度参数和基本能量分析的基础上的稀疏波结构。
It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected to a vacuum. Given a rarefaction wave with one-side vacuum state to the compressible Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier–Stokes equations which converge to the above rarefaction wave with vacuum as the viscosity tends to zero. Moreover, the uniform convergence rate is obtained. The proof consists of a scaling argument and elementary energy analysis based on the underlying rarefaction wave structures.