Approximation of a simple Navier-Stokes model by monotonic rearrangement

Yann Brenier (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application of a suitable monotonic rearrangement operator In addition, our result can be easily extended to a related Navier-Stokes-Poisson system.

Mots clés: fluid mechanics; monotonic rearrangement; optimal transport; systems of particles

Domaines: Equations aux dérivées partielles [math.AP]

Yann Brenier. Approximation of a simple Navier-Stokes model by monotonic rearrangement. 2012. ⟨hal-00749578⟩