From: BrendaSueCook (brenda@math.missouri.edu)
Date: Tue Apr 17 2007 - 08:31:34 CDT
Colloquium
Department of Mathematics
A.V. Fursikov
Moscow State University
Stabilization of the Navier-Stokes
equations with the help
of a boundary feed-back control
Abstract:
Let $\hat v$ be an unstable steady-state solution of the Navier-Stokes
equations
on a bounded domain $\Omega$. The stabilization problem consists of
finding
a Dirichlet boundary control for a given initial condition $v_0$ close to
$\hat v$ such that the solution of the resulting boundary value problem
tends
exponentially
to $\hat v$ as $t \to \infty$.
The control should satisfy the feed-back property, i.e. it should react
to unpredictable fluctuations of a solution by damping them.
In this talk we shall present the construction of such a feed-back control,
the stabilization mechanism, and the retention of the the stabilized
solution
near $\hat v$. We will also present some initial steps towards the
solution
of the non-local stabilization problem (when the initial condition $v_0$
is not
close to $\hat v$).
Thursday, April 19
3:30 p.m.
114 General Classroom Building
Refreshments will be served at 3:00 p.m.
in Room 326 Mathematical Sciences (Math Lounge).
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