Well Posedness for Pressureless Flow |
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| Authors: | Feimin Huang Zhen Wang |
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| Institution: | (1) S.I.S.S.A., Via Beirut 2–4, 34010 Trieste, Italy, IT;(2) Institute of Applied Mathematics, Academia Sinica, Beijing 100080, P.R. China, CN;(3) Department of Mathematics, City University of Hong Kong, Hong Kong, P.R. China, CN |
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| Abstract: | 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 in the same functional space as the existence theorem.
Received: 26 September 2000 / Accepted: 25 April 2001 |
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