The initial boundary value problem for Navier-Stokes equations

By making full use of the estimates of solutions to nonstationary Stokes eq uations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equations in arbit rary three dimensional domain with uniformly C-3 boundary, under the assump tion that parallel to a parallel to L-2(Omega) + parallel to f parallel to L-1 (0,infinity;L-2(Omega)) or parallel to del a parallel to L-2(Omega) + p arallel to f parallel to L-2(0,infinity;L-2(Omega)) small or viscosity nu l arge. Here a is a given initial velocity and f is the external force. This improves on the previous results. Moreover, the solvability of the case wit h nonhomogeneous boundary conditions is also discussed.