Nonlocal abstract Stokes equations and applications

In this paper, the Cauchy problem for the stationary and instationary nonlocal imcompressible abstract Stokes equation is considered. The equation involve a convolution term and an abstract operator in a Banach space E on leading part. The existence, uniqueness and coercive estimates are derived in L p spaces. We, can obtain different classes of 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 L p -maximal regularity properties to solution of initial value problems for nonlocal degenerate Stokes equations and nonlocal Stokes equations with discontinuous coefficients are established AMS: 35Q30, 76D05, 34G10, 35J25