TY - JOUR
T1 - Local boundary regularity for the Navier-Stokes equations in nonendpoint borderline Lorentz spaces
AU - Barker, Tobias
PY - 2017/6/5
Y1 - 2017/6/5
N2 - Local regularity up to the flat part of the boundary is proved for certain classes of distributional solutions that are L∞L3,q with q finite. The corresponding result for the interior case was recently proved by Wang and Zhang, see also Phuc’s paper. For local regularity up to the flat part of the boundary, q = 3 was established by G. A. Seregin. Our result can be viewed as an extension of it to L3,q with q finite. New scale-invariant bounds, refined pressure decay estimates near the boundary and development of a convenient new ϵ-regularity criterion, are central themes in providing this extension.
AB - Local regularity up to the flat part of the boundary is proved for certain classes of distributional solutions that are L∞L3,q with q finite. The corresponding result for the interior case was recently proved by Wang and Zhang, see also Phuc’s paper. For local regularity up to the flat part of the boundary, q = 3 was established by G. A. Seregin. Our result can be viewed as an extension of it to L3,q with q finite. New scale-invariant bounds, refined pressure decay estimates near the boundary and development of a convenient new ϵ-regularity criterion, are central themes in providing this extension.
U2 - 10.1007/s10958-017-3424-2
DO - 10.1007/s10958-017-3424-2
M3 - Article
SN - 1072-3374
VL - 224
SP - 391
EP - 413
JO - Journal of Mathematical Sciences N.Y.
JF - Journal of Mathematical Sciences N.Y.
IS - 3
ER -