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Regularity Criteria in Weak L3 for 3D Incompressible Navier-Stokes Equations
2015
Funkcialaj Ekvacioj
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We study the regularity of a distributional solution ðu; pÞ of the 3D incompressible evolution Navier-Stokes equations. Let B r denote concentric balls in R 3 with radius r. We will show that if p A L m ð0; 1; L 1 ðB 2 ÞÞ, m > 2, and if u is su‰ciently small in L y ð0; 1; L 3; y ðB 2 ÞÞ, without any assumption on its gradient, then u is bounded in B 1 Â ð1=10; 1Þ. It is an endpoint case of the usual Serrin-type regularity criteria, and extends the steady-state result of Kim-Kozono to the time
doi:10.1619/fesi.58.387
fatcat:h5mhprf74rgaromkqkz74m7rni