On Unique Continuation for Navier-Stokes Equations

Abstract

We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different times t0=0 and t1=1 which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.