Initial and boundary value problem of the unsteady Navier-Stokes system in the half-space with Holder continuous boundary data

We study the initial boundary value problem of the Navier Stokes system in the half-space. We prove the unique solvability of the weak solution for some short time interval (0, T) with the velocity in C-alpha,C-alpha/2 (R-+(n) x (0,T)), 0 < alpha < 1, when the given initial data in C-alpha(R-+(n)) and the given boundary data in C-alpha,C-alpha/2(Rn-1 x (0, T)) satisfy the compatibility conditions. Our result generalizes the result in [29] considering nonhomogeneous Dirichlet boundary data. (C) 2015 Elsevier Inc. All rights reserved.