On unique continuation for Navier-Stokes equations (Q2520475)

Summary: 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 \(t_0 = 0\) and \(t_1 = 1\) which guarantee the ``global'' unique continuation of solutions for the Navier-Stokes equations.