Some Recent Results on Feedback
نویسندگان
چکیده
In this paper we present several results from our recent work 1] concerning feedback control of the three-dimensional Navier-Stokes system on a bounded domain with non-slip boundary conditions. The feedback is introduced in the form of an additional nonlinear viscosity term which is nonvanishing only on a subdomain of the main domain and is proportional to the energy dissipation functional on this subdomain. For the controlled system, in 1] we prove the existence, uniqueness and stability of the strong solution for initial data and forcing term which are arbitrary on the subdomain of control and are suuciently small (in appropriate function spaces) outside this subdomain.
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