Solvability of the Navier-Stokes system with L-2 boundary data

We prove the existence of the very weak solution of the Dirichlet problem f or the Navier-Stokes system with L-2 boundary data. Under the small data as sumption we also prove the uniqueness. We use the penalization method to st udy the linearized problem and then apply Banach's fixed point theorem for the nonlinear problem with small boundary data. We extend our result to the case with no small data assumption by splitting the data on a large regula r and small irregular part.