an:06144785
Zbl 1260.35125
Neustupa, Ji????
A note on local interior regularity of a suitable weak solution to the Navier-Stokes problem
EN
Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1391-1400 (2013).
00315709
2013
j
35Q30 76D03 76D05
Navier-Stokes equations; suitable weak solution; regularity
Summary: We formulate a criterion which guarantees a local regularity of a suitable weak solution \(v\) to the Navier-Stokes equations (in the sense of \textit{L. Caffarelli, R. Kohn} and \textit{L. Nirenberg} [Commun. Pure Appl. Math. 35, 771--831 (1982; Zbl 0509.35067)]). The criterion shows that if \((x_0, t_0)\) is a singular point of solution \(v\) then the \(L^3\)-norm of \(v\) concentrates in an amount greater than or equal to some \(\epsilon > 0\) in an arbitrarily small neighbourhood of \(x_0\) at all times \(t\) in some left neighbourhood of \(t_0\). As a partial result, we prove that a localized solution satisfies the strong energy inequality.
Zbl 0509.35067