Non-formation of vacuum states for compressible Navier-Stokes equations
Non-formation of vacuum states for compressible Navier-Stokes equations
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DOI：
10.1007/s002200000322
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发表时间：
2001-02-01
影响因子：
2.4
通讯作者：
Smoller, J
中科院分区：
文献类型：
--
作者：
Hoff, D;Smoller, J
我们证明了一维空间中可压缩流体流动的Navier-Stokes方程的弱解不具有真空态，只要初始不存在真空态。我们考虑的解和外力是相当普遍的：基本要求是流体的质量和能量密度在每个时刻都是局部可积的，并且速度梯度的L-loc（2）-范数在时间上是局部可积的。我们的分析表明，如果出现真空状态，粘性力将对相邻流体施加无限大的脉冲，从而违反动量保持局部有限的假设。
We prove that weak solutions of the Navier-Stokes equations for compressible fluid flow in one space dimension do not exhibit vacuum states, provided that no vacuum states are present initially. The solutions and external forces that we consider are quite general: the essential requirements are that the mass and energy densities of the fluid be locally integrable at each time, and that the L-loc(2)-norm of the velocity gradient be locally integrable in time. Our analysis shows that, if a vacuum state were to occur, the Viscous force would impose an impulse of infinite magnitude on the adjacent fluid, thus violating the hypothesis that the momentum remains locally finite.