Title: Hydrodynamical limits : from Boltzmann to Navier-Stokes

Abstract : It is well-known that kinetic equations (including Boltzmann with or without cutoff assumption and Landau equations) are related to the incompressible Navier-Stokes equation, in the limit when the Mach and the Knudsen numbers go to zero. In the framework of strong solutions, many results in the litterature assume a smallness condition on the initial data in order to make this convergence rigourous, regardless of the space dimension -- despite the fact that the incompressible Navier-Stokes equation is known to be globally well posed in two space dimensions for instance, without any smallness assumption. The regularity imposed on the initial data is also usually much higher than that required to solve the Navier-Stokes equation.

In this talk we shall survey some recent results on the subject, where the emphasis is put on bridging the gap between the assumptions made on the initial data for Boltzmann and for Navier-Stokes. This corresponds to joint works with Kleber Carrapatoso and Isabelle Tristani. 

Bio : Isabelle Gallagher obtained her PhD under the supervision of Jean-Yves Chemin at Paris 6 University (now Sorbonne Université) in 1998. She then held a CNRS position in Orsay and École polytechnique, before moving in 2004 to Paris 7 University (now Université Paris Cité) where she is Professor. She was on leave at the École Normale Supérieure in Paris from 2017 to 2025. She is currently head of the French Mathematical Society. She studies Partial Differential Equations, with a special interest for fluid mechanics, kinetic equations, and their link with particle systems. She was invited speaker at ECM in 2012 and ICM in 2014.  She was awarded the Erwin Schrödinger Institute for Mathematics and Physics Medal in 2023.