Nonlocal abstract Stokes equations and applications

Abstract

In this talk, the Cauchy problem for the stationary and instationary nonlocal imcompressible abstract Stokes equations are considered. The equation involve the the convolution term and abstract operator in a Banach space E on leading part. The existence, uniqueness and coercive esimates in Lp spaces is derived. We can obtain a di§erent classes Novier-Stokes equations by choosing the space E and the linear operator A which occur in a wide variety of physical systems. In application the existence, uniqueness and Lp-maximal regularity properties to solution of mixed problems for nonlocal degenerate Navier-Stokes equations and nonlocal Navier-Stokes equations with discontinuous coe¢ cients are established.