Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

In the physical sciences, relaxation usually means the return of a perturbed system to equilibrium. Each relaxation process can be categorized by a relaxation time $\tau$, for a generic commercial grade ferrofluid (a mixture  of nanoscale ferromagnetic particles of a compound containing iron suspended in a fluid) the relaxation time is very small, of the order $\tau \sim 10^{-9}$; it makes hence sense to provide an asymptotic approximation when $\tau  \to 0$. In this talk I will explain how to construct solutions for the Shliomis model of ferrofluids in a critical space of infinite $L^2$ energy uniformly for $\tau\in \left(0, \tau_0\right)$, such uniform construction will allow us to study the limit regime $\tau \to 0$ and the convergence of the critical solutions.