[PDF] On well-posedness for thick spray equations-论文阅读讨论-ReadPaper

摘要

In this paper, we prove the local in time well-posedness of thick sprayequations in Sobolev spaces, for initial data satisfying a Penrose-typestability condition. This system is a coupling between particles described by akinetic equation and a surrounding fluid governed by compressible Navier-Stokesequations. In the thick spray regime, the volume fraction of the dispersedphase is not negligible compared to that of the fluid. We identify a suitable stability condition bearing on the initial conditionsthat provides estimates without loss, ensuring that the system is well-posed.It coincides with a Penrose condition appearing in earlier works on singularVlasov equations. We also rely on crucial new estimates for averagingoperators. Our approach allows to treat many variants of the model, such ascollisions in the kinetic equation, non-barotropic fluid or density-dependentdrag force.

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