On the pressure regularity criterion of the 3D Navier–Stokes equations
Journal of Mathematical Analysis and Applications(2012)
Abstract
In the study of regularity criteria for the weak solutions of the 3D Navier–Stokes equations, an improved regularity criterion is obtained. More precisely, it is proved that if the pressure satisfies the critical growth condition π(x,t)∈L22+r(0,T;Ḃ∞,∞r(R3))for −1≤r≤1, then the weak solution u(x,t) is regular on (0,T]. The finding is mainly based on the innovative function decomposition methods together with Besov space techniques.
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Key words
Navier–Stokes equations,Regularity criterion,Pressure,Besov spaces
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