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 $/tau /approx 10^{-9}$; 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 $L2$ energy uniformly for $/tau/in (0, /tau_0)$, such uniform construction will allow us to study the limit regime $/tau /to 0$ and the convergence of the critical solutions.

海报