Logarithmically improved extension criteria involving the pressure for the Navier–Stokes equations in Rn$\mathbb {R}^{n}$

Abstract

AbstractWe consider the Cauchy problem of the Navier–Stokes equations in ( and establish several new extension criteria involving the pressure or its gradient. In particular, we improve the previous results by means of the homogeneous Besov space with negative differential orders in the case . Our method is based on the interpolation inequality and the trilinear estimate due to Gérard–Meyer–Oru (Séminaire É. D. P. (1996–1997), Exp. No. IV, 1–8) and Guo–Kučera–Skalák (J. Math. Anal. Appl. 458 (2018) 755–766), respectively.