Fursikov, A. V.; Imanuvilov, O. Yu. Local exact boundary controllability of the Boussinesq equation. (English) Zbl 0907.76020 SIAM J. Control Optimization 36, No. 2, 391-421 (1998). Summary: We study the local exact boundary controllability problem for the Boussinesq equations that describe an incompressible fluid flow coupled to thermal dynamics. The result that we get in this paper is as follows: suppose that \(\widehat y(t,x)\) is a given solution of the Boussinesq equation where \(t \in(0,T)\), \(x \in \Omega\), \(\Omega\) is a bounded domain with \(C^\infty\)-boundary \(\partial \Omega\). Let \( y_0(x)\) be a given initial condition and \(\| \widehat y(0,\cdot) - y_0 \| < \varepsilon\) where \(\varepsilon=\varepsilon(\widehat y)\) is small enough. Then there exists boundary control \(u\) such that the solution \(y(t,x)\) of the Boussinesq equations satisfying \(y |_{(0,T) \times \partial \Omega} = u\), \(y |_{t=0} = y_0\) coincides with \(\widehat y(t,x)\) at the instant \(T\) : \(y(T,x) \equiv \widehat y(T,x)\). Cited in 21 Documents MSC: 76D99 Incompressible viscous fluids 49J20 Existence theories for optimal control problems involving partial differential equations 93B05 Controllability 93C20 Control/observation systems governed by partial differential equations Keywords:thermal dynamics × Cite Format Result Cite Review PDF Full Text: DOI