TY - JOUR
T1 - Interior regularity criteria in weak spaces for the Navier-Stokes equations
AU - Kim, Hyunseok
AU - Kozono, Hideo
PY - 2004/9/1
Y1 - 2004/9/1
N2 - We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Ω × (0, T), where Ω ⊂ R 3 and 0 < T < ∞. The local boundedness of a weak solution u is proved under the assumption that ||u||Lws(0, T; Lwr (Ω)) is sufficiently small for some (r, s) with 2/s + 3/r = 1 and 3 ≤ r ≤ ∞. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.
AB - We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Ω × (0, T), where Ω ⊂ R 3 and 0 < T < ∞. The local boundedness of a weak solution u is proved under the assumption that ||u||Lws(0, T; Lwr (Ω)) is sufficiently small for some (r, s) with 2/s + 3/r = 1 and 3 ≤ r ≤ ∞. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.
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U2 - 10.1007/s00229-004-0484-7
DO - 10.1007/s00229-004-0484-7
M3 - Article
AN - SCOPUS:4744359714
SN - 0025-2611
VL - 115
SP - 85
EP - 100
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 1
ER -