{"id":13097,"date":"2017-05-24T16:57:04","date_gmt":"2017-05-24T12:57:04","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?p=13097"},"modified":"2017-05-26T13:58:02","modified_gmt":"2017-05-26T09:58:02","slug":"the-institute-seminar-on-one-optimal-control-problem-for-navier-stokes-system-was-held","status":"publish","type":"post","link":"https:\/\/www.imm.az\/exp\/2017\/05\/24\/the-institute-seminar-on-one-optimal-control-problem-for-navier-stokes-system-was-held\/","title":{"rendered":"The Institute seminar on \u201cOne optimal control problem for Navier-Stokes system\u201d was held"},"content":{"rendered":"

Today at the Institute seminar professor of M.V. Lomonosov Moscow state University Andrey V.Fursikov gave a talk on \u201cOne optimal control problem for Navier-Stokes system\u201d.
\nIn the talk one optimal boundary control problem for the three-dimensional, evolutionary Navier-Stokes equations in an exterior of bounded domain \u03a9 is considered. The control objective is to minimize the drag functional, and control is effected through the Dirichlet boundary condition on d\u03a9.
\nFirst of all the proper space of vector-fields on boundary d\u03a9 where we look for the control is found. Adding the norm of this space as a term of the cost functional well-posedness of considered optimal control problem is obtained. The existence of an optimal solution is proved. A strong form of an optimality system of equations is derived.
\nThese results are based on a specially created theory of boundary value problems for Navier-Stokes equations with non zero boundary condition belonging to a non standard space of traces . Derivation of optimality system is based also on regularity results for the adjoint Oseen equations with regular initial data which do not satisfy the compatibility conditions.<\/p>\n