Well Posedness for Pressureless Flow
Well Posedness for Pressureless Flow
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DOI：
10.1007/s002200100506
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发表时间：
2001-08
影响因子：
2.4
通讯作者：
F. Huang;Zhen Wang
中科院分区：
文献类型：
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作者：
F. Huang;Zhen Wang
研究了无压气体的唯一性问题。以前的结果在这个主题上是已知的情况下，当初始数据被假定为一个有界的可测函数。这个假设是不自然的，因为解一般是拉东测度。本文证明了当初始数据为Radon测度时，弱解的唯一性。我们发现，除了Oleinik熵条件，它也是重要的，要求能量是弱连续的初始。我们的唯一性结果是在与存在性定理相同的泛函空间中得到的。
We study the uniqueness problem for pressureless gases. Previous results on this topic are only known for the case when the initial data is assumed to be a bounded measurable function. This assumption is unnatural because the solution is in general a Radon measure. In this paper, the uniqueness of the weak solution is proved for the case when the initial data is a Radon measure. We show that, besides the Oleinik entropy condition, it is also important to require the energy to be weakly continuous initially. Our uniqueness result is obtained inthe same functional spaceas the existence theorem.