AN OPEN MAPPING THEOREM FOR THE NAVIER-STOKES EQUATIONS

摘要

We consider the Navier-Stokes equations in the layer ?~n x [0, T] over ?~n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I + K)u =f, where K is a compact continuous operator in anisotropic normed Holder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t ? [0, T].