Applied Mathematics Seminar
Maria Schonbek
University of California, Santa Cruz
$L^2$ asymptotic stability of mild solutions to the Navier-Stokes system
Abstract: We consider the initial value problem for the Navier-Stokes equations modeling an incompressible fluid in three dimensions:
$$
u_t + u\cdot \nabla u +\nabla p = \Delta u +F,\;\;\; (x,t) \in \mathbb{R}^3\times (0,\infty),
$$
$$
\mbox{div}\; u=0\,,
$$
$$
u(x,0) =u_0(x)\,.
$$
It is well-known that this problem has a unique global-in-time mild solution for a sufficiently
small initial condition $u_0$ and for a small external force $F$ in suitable scaling
invariant spaces. We show that these global-in-time mild solutions are asymptotically
stable under every (arbitrary large) $L^2$-perturbation of their initial conditions.
Monday April 21, 2014 at 4:00 PM in SEO 636