On linearization principle for Navier-Stokes system with dynamic slip boundary condition

We consider incompressible Navier-Stokes equations in a bounded 3D regular domain, coupled with the so-called dynamic boundary condition. rigorously establish principle of linearized stability. Namely, given smooth stationary state, we prove that equation has complete basis generalized eigenfunctions, and non-linear stability depends on supremum real part spectrum usual way. work class weak solutions satisfying energy inequality, for which global existence (but not uniqueness) is known.