On a bounded shear flow in half-space

In this paper we describe a simple shear flow in half-space which has interesting properties from the point of view of boundary regularity. It is a solution with bounded velocity field to both the homogeneous Stokes system and the Navier–Stokes equation, and satisfies the homogeneous initial and boundary conditions. The gradient of the solution can become unbounded near the boundary. The example significantly simplifies an earlier construction by K. Kang, and shows that the boundary estimates obtained in [3] are sharp. Bibl. 4 titles.