The initial value problem for the Navier-Stokes equations with general slip boundary condition in Hölder spaces (Q1402391)

The authors study the initial-boundary value problem for incompressible Navier-Stokes equations with general slip boundary condition on a solid boundary. The unique solvability is established in anisotropic Hölder spaces locally in time for three-dimensional problem, and globally in time for two-dimensional problem without smallness restrictions. The authors approximate the solutions of Navier-Stokes systems by solutions of a linearized homogeneous Stokes-type system, and then prove the convergence of successive approximations.