Decay of solutions for 2D Navier-Stokes equations posed on Lipschitz and smooth bounded and unbounded domains (Q1732148)

The present paper deals with the four initial-boundary value problems for the 2D Navier-Stokes equations posed on a rectangle, on a half-strip, on a bounded smooth domain, on an unbounded smooth domain. The existence and uniqueness of strong solutions are established. It is proved that strong solutions in unbounded domains are regular in smooth bounded subdomains, the decay rate is different for different norms, depending on the geometrical characteristics of the domains. The existence of an unique global regular solution, which decays exponentially as \(t\rightarrow +\infty\), is proved. Sharp estimates for the exponential decay rates of solutions to initial-boundary value problems for the 2D Navier-Stocks equations are determined.