TY - JOUR
T1 - On a bounded shear flow in a half-space
AU - Seregin, G.
AU - Sverak, V.
PY - 2011/10
Y1 - 2011/10
N2 - In this paper, a simple shear flow in a half-space, which has interesting properties from the point of view of boundary regularity, is described. It is a solution with a 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 may become unbounded near the boundary. The example significantly simplifies an earlier construction by K. Kang, and shows that the boundary estimates obtained in a recent paper by the first author are sharp. Bibliography: 4 titles.
AB - In this paper, a simple shear flow in a half-space, which has interesting properties from the point of view of boundary regularity, is described. It is a solution with a 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 may become unbounded near the boundary. The example significantly simplifies an earlier construction by K. Kang, and shows that the boundary estimates obtained in a recent paper by the first author are sharp. Bibliography: 4 titles.
UR - http://www.scopus.com/inward/record.url?scp=80053505556&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80053505556&partnerID=8YFLogxK
U2 - 10.1007/s10958-011-0552-y
DO - 10.1007/s10958-011-0552-y
M3 - Article
AN - SCOPUS:80053505556
SN - 1072-3374
VL - 178
SP - 353
EP - 356
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 3
ER -