Global solutions of the equations of one-dimensional, compressible flow with large data and forces, and with differing end states
Global solutions of the equations of one-dimensional, compressible flow with large data and forces, and with differing end states
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DOI：
10.1007/s000330050120
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发表时间：
1998-09
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影响因子：
--
通讯作者：
D. Hoff
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文献类型：
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作者：
D. Hoff
在初始数据、状态方程和外力的最小假设条件下，证明了一维空间可压缩流的Navier-Stokes方程解的整体存在性。具体地说，我们只要求初始数据的密度在远离零的上下有界，并且密度和速度在l2中，模态恒定在和，这可能是不同的。在数据和外力上都没有小的假设。特别地，我们包括了初始数据是具有任意大跳跃不连续的分段常数的重要情况。我们的结果表明，即使在这种一般性下，在有限时间内也不能形成真空态和集中态。
We prove the global existence of solutions of the Navier–Stokes equations of compressible flow in one space dimension with minimal hypotheses on the initial data, the equation of state, and the external force. Specifically, we require of the initial data only that the density be bounded above and below away from zero, and that the density and velocity be inL2, modulo constant states atand, which may be different. There are no smallness hypotheses on either the data or on the external force. In particular, we include the important case that the initial data is piecewise constant with arbitrarily large jump discontinuities. Our results show that, even in this generality, neither vacuum states nor concentration states can form in finite time.