On the Controllability of the Hydrostatic Stokes Equations

Springer Science and Business Media LLC - Tập 10 - Trang 402-422 - 2007
S. Guerrero1, F. Guillén-González2
1Université Pierre et Marie Curie-Paris 6, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, France
2Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Sevilla, Spain

Tóm tắt

This paper is devoted to present some results on the controllability of the hydrostatic Stokes equations. The first main result of this paper states that the approximate null controllability of this system holds. This is proved whatever the boundary conditions are. Then, we extend this result to an exact null controllability result when the boundary conditions are ∂ z u = 0 (the vertical derivative of the horizontal velocity) at the bottom.