Nonlocal abstract Stokes operators and applications

In this paper, the Cauchy problem for the stationary and nonstationary nonlocal incompressible abstract Stokes equation is considered. The equation involves a convolution term and an abstract operator in a Banach space E. Existence, uniqueness, and coercive estimates are derived in L p spaces. Different classes of Stokes equations can be obtained by choosing the space E and the linear operator A, which occur in a wide variety of physical systems. As an application of the obtained results, the existence, uniqueness, and L p -maximal regularity properties of solutions to initial value problems for nonlocal degenerate Stokes equations and nonlocal Stokes equations with discontinuous coefficients are established.