Convex hulls, sticky particle dynamics and pressure-less gas system. (English) Zbl 1153.76062
Summary: We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities with negative jumps. We show the existence of a stochastic process and a forward flow satisfying and , where is the law of and is the velocity of particle at time . Results on the flow characterization and Lipschitz continuity are also given. Moreover, the map is the entropy solution of a scalar conservation law , where the flux represents the particles momentum, and is a weak solution of the pressure-less gas system of equations of initial datum .
|76T15||Dusty-gas two-phase flows|
|76M35||Stochastic analysis (fluid mechanics)|
|60H30||Applications of stochastic analysis|
|60H15||Stochastic partial differential equations|