Weighted estimates for nonstationary Navier-Stokes equations in exterior domains
For nonstationary incompressible Navier-Stokes equations in a three-dimensional exterior domain, the authors derive new a priori estimates in some weighted spaces. Basing on these estimates, the authors establish existence and uniqueness of strong solutions in the weighted spaces, as well as prove some decay properties. The technique employed relies upon the representation of pressure in terms of fundamental solution to Laplace equation, using the singular integral theory. The estimates then follow from estimates for approximate solutions of a linearized problem.
nonstationary incompressible Navier-Stokes equations
scientific article; zbMATH DE number 1757311