TY - JOUR
T1 - On regularity criteria in conjunction with the pressure of the Navier-Stokes equations
AU - Kang, Kyungkeun
AU - Lee, Jihoon
PY - 2006
Y1 - 2006
N2 - We present new regularity criteria involving the integrability of the pressure for the Navier-Stokes equations in bounded domains with smooth boundaries.We prove that either if the pressure belongs to L x,t γ,q with 3/γ+2/q≤2 and 3/2<γ≤∞ or if the gradient of the pressure belongs to L x,t γ,q with 3/γ+2/q≤2 and 1<γ≤∞, then weak solutions are regular. Local regularity criteria in terms of pressure are also established near a flat boundary as well as in the interior for suitable weak solutions.
AB - We present new regularity criteria involving the integrability of the pressure for the Navier-Stokes equations in bounded domains with smooth boundaries.We prove that either if the pressure belongs to L x,t γ,q with 3/γ+2/q≤2 and 3/2<γ≤∞ or if the gradient of the pressure belongs to L x,t γ,q with 3/γ+2/q≤2 and 1<γ≤∞, then weak solutions are regular. Local regularity criteria in terms of pressure are also established near a flat boundary as well as in the interior for suitable weak solutions.
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U2 - 10.1155/IMRN/2006/80762
DO - 10.1155/IMRN/2006/80762
M3 - Article
AN - SCOPUS:33749529740
VL - 2006
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
M1 - 80762
ER -