Long-time behavior of periodic Navier-Stokes equations in critical spaces

摘要

We establish smoothing effects for the 3-D incompressible periodic Navier-Stokes equations for initial data in the critical Sobolev space H~(1/2)(T~3).We use this to prove that any global solution to the 3D periodic NSE decays exponentially fast to zero as time tends to infinity, as soon as the data (hence the solution) is mean free. Otherwise, the difference to the average do so.