A Navier-Stokes type problem with high order elliptic operator and applications

The existence, uniqueness and uniformly $L^p$ estimates for solutions of high order abstract 2 Navier-Stokes problem on half space are derived. The equation involve 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 class of Navier-Stokes type problems are obtained. In application the existence, uniqueness and uniformly L^p estimates for solution of the Wentzell-Robin type mixed problem for Navier-Stokes equation and mixed problem for degenerate Navier-Stokes equations are 8 established.