In this paper, 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 on some short time interval (0, T) with the velocity in $C^{ \alpha, \frac12 \alpha} ({ \mathbb R}^n_+ \times (0, T)), 0 < \alpha < 1$, when the given initial data is in $C^\alpha ({ \mathbb R}^n_+)$ and the given boundary data is in $C^{ \alpha, \frac12 \alpha} ({ \mathbb R}^{ n-1} \times (0, T))$. Our result generalizes the result in [30] considering nonhomogeneous Dirichlet boundary data.
Categories: math.AP