Speaker
Charles Elbar, LJLL Sorbonne Universite
Abstract
The Vlasov-Cahn-Hilliard model was introduced by Noguchi and Takata in 2018. In the limit when the Knudsen number goes to 0 (hydrodynamic limit), they proved formally that the model converges to the Cahn-Hilliard equation, that has been widely used in biology and physics. We give some ideas, using a two-step approximation to prove the statement rigorously. First, we mollify the force and pass to the limit in the Vlasov equation. Then we remove the mollifications and prove convergence to the Cahn-Hilliard equation using commutator estimates.