Probabilistic model associated with the pressureless gas dynamics

Details Probabilistic model associated with the pressureless gas dynamics Probabilistic model associated with the pressureless gas dynamics

2009-08-14

arxiv.org/abs/0908.2084v2

Mathematics

Analysis of PDEs

28 pages, submitted

Scientific paper

Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the pressureless gas dynamics describing sticky particles. As a bridging step we consider a medium consisting of noninteracting particles. We analyze the difference in the behavior of discontinuous solutions for these two models and the relations between them. In our framework we obtain a unique entropy solution to the Riemann problem in 1D case. Moreover, we describe how starting from smooth data a $\delta$ - singularity arises in one component of the solution.

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