Abstract
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 \(E\) . 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.
