MATHEMATICS COLLOQUIUM
Speaker: Catalin Trenchea
Title: Velocity and Magnetic Field Tracking for MHD Flows
Affiliation: Florida State University
Date: Friday, January 27, 2006.
Place and Time: Room 101 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract.
We consider a viscous, incompressible, electrically conducting fluid
in a bounded two-dimensional domain. We assume that the flow is
governed by the Navier-Stokes equations, and magnetic field by
Maxwell's equations. The initial condition of the flow is known and
it is desired to force the system to a desired behavior called
"target". For this purpose the right hand sides of both equations
can be specified. The optimal control problem seeks to minimize the
discrepancies between flow and target over time.
Existence of optimal solutions is proved and first-order necessary
conditions for optimality are used to derive an optimality system of
partial differential equations whose solutions provide optimal states
and controls.
We also analyze a modified Navier-Stokes equation coupled with
Maxwell's equation in three dimensions. The existence of optimal
solutions is shown, the Gateux differentiability for the MHD system
with respect to controls is proved, and the optimality system is
derived.
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