Boundary stabilization of a 3-D Navier Stokes flow in the neighborhood of an unstable equilibrium

Połączone seminarium:  Równania Fizyki Matematycznej i Biomatematyka i Teoria Gier

We shall consider a 3-D Navier Stokes flow defined in the neighborhood of an unstable equilibrium. For large Reynolds numbers, the steady state solutions are unstable and cause turbulence in their surroundings. Our goal is to construct a feedback operator, supported on the boundary of the domain, which will produce local exponential stability of such steady-state solution. The construction is based on solvability of optimization problem with "high" gain (unbounded) functional cost. This leads to the analysis of existence and uniqueness of the associated non-standard Riccati equations with boundary controls.