Geodesic
On a bounded shear flow in half-space
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 200-205 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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G. Seregin; V. Sverak. On a bounded shear flow in half-space. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 200-205. http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a8/

[1] K. Kang, “Unbounded normal derivative for the Stokes system near boundary”, Math. Ann., 331 (2005), 87–109 | DOI | MR | Zbl

[2] G. Seregin, “Local regularity theory of the Navier–Stokes equations”, Handbook of Mathematical Fluid Mechanics, v. 4, eds. Friedlander, D. Serre, 159–200

[3] G. Seregin, “A note on local boundary regularity for the Stokes system”, Zap. Nauchn. Semin. POMI, 370, 2009, 151–159

[4] J. Serrin, “On the interior regularity of weak solutions of the Navier–Stokes equations”, Arch. Ration. Mech. Anal., 9 (1962), 187–195 | DOI | MR | Zbl