Nonlocal Navier-Stokes problem with a small parameter
Department of Mechanical Engineering, Okan University, Akfirat, Tuzla, Istanbul, Turkey
Institute of Mathematics and Mechanics, Azerbaijan National Akademy of Science, Baku, Azerbaijan
Boundary Value Problems 2013, 2013:107 doi:10.1186/1687-2770-2013-107Published: 26 April 2013
Initial nonlocal boundary value problems for a Navier-Stokes equation with a small parameter is considered. The uniform maximal regularity properties of the corresponding stationary Stokes operator, well-posedness of a nonstationary Stokes problem and the existence, uniqueness and uniformly estimates for the solution of the Navier-Stokes problem are established.
MSC: 35Q30, 76D05, 34G10, 35J25.