MATHEMATICS, vol.8, no.12, pp.1-23, 2020 (SCI-Expanded)
The existence, uniqueness and uniformly L-p estimates for solutions of a high-order abstract Navier-Stokes problem on half space are derived. The equation involves an abstract operator in a Banach space E and small parameters. Since the Banach space E is arbitrary and A is a possible linear operator, by choosing spaces E and operators A, the existence, uniqueness and L-p estimates of solutions for numerous classes of Navier-Stokes type problems are obtained. In application, the existence, uniqueness and uniformly L-p estimates for the solution of the Wentzell-Robin-type mixed problem for the Navier-Stokes equation and mixed problem for degenerate Navier-Stokes equations are established.