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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:

35L65 Hyperbolic conservation laws
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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