Local exact boundary controllability of the Boussinesq equation

摘要

We study the local exact boundary controllability problem for the Boussinesq equations that describe an incompressible fluid ow coupled to thermal dynamics. The result that we get in this paper is as follows: suppose that (y) over cap(t, x) is a given solution of the Boussinesq equation where t is an element of (0, T), x is an element of Omega, Omega is a bounded domain with C-infinity-boundary partial derivative Omega. Let y(0)(x) be a given initial condition and (y) over cap 0, .) - y(0) < epsilon where epsilon = epsilon((y) over cap) is small enough. Then there exists boundary control u such that the solution y(t; x) of the Boussinesq equations satisfying y((0, T) x partial derivative Omega) = u, y(t=0) = y(0) coincides with (y) over cap(t, x) at the instant T : y(T;x) = (y) over cap(T, x). [References: 38]