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Well posedness for pressureless flow. (English) Zbl 0988.35112
This paper considers the one-dimensional pressureless gases and studies the uniqueness of weak solutions when the initial data is a Radon measure. It is shown that besides the Oleinik entropy condition, it is important to require the energy to be weakly continuous initially; and without this energy condition, the weak solution satisfying the Oleinik entropy condition is not unique. The paper should be of interest to someone working on weak solutions of conservation laws.
MSC:
35L65Conservation laws
35A05General existence and uniqueness theorems (PDE) (MSC2000)
76N10Compressible fluids, general
35B30Dependence of solutions of PDE on initial and boundary data, parameters