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.