On the convergence of smooth solutions from Boltzmann to Navier-Stokes

Isabelle Gallagher (1) , Isabelle Tristani (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

In this work, we are interested in the link between strong solutions of the Boltzmann and the Navier-Stokes equations. To justify this connection, our main idea is to use information on the limit system (for instance the fact that the Navier-Stokes equations are globally wellposed in two space dimensions or when the initial data is small). In particular we prove that the life span of the solutions to the rescaled Boltzmann equation is bounded from below by that of the Navier-Stokes system. We deal with general initial data in the whole space in dimensions 2 and 3, and also with well-prepared data in the case of periodic boundary conditions.

Domaines: Equations aux dérivées partielles [math.AP]

Isabelle Gallagher, Isabelle Tristani. On the convergence of smooth solutions from Boltzmann to Navier-Stokes. Annales Henri Lebesgue, In press, ⟨10.5802/ahl.40⟩. ⟨hal-02057498v2⟩