On anisotropic regularity criteria for the solutions to 3D Navier–Stokes equa- tions Patrick Penel and Milan Pokorn´ y Abstract. In this short note we consider the 3D Navier–Stokes equations in the whole space, for an incompressible fluid. We provide sufficient conditions for the regularity of strong solutions in terms of certain com- ponents of the velocity gradient. Based on the recent results from [6] we show these conditions as anisotropic regularity criteria which partially interpolate results from [6] and older results of similar type from [12]. Mathematics Subject Classification (2010). Primary 35Q30; Secondary 76D05. Keywords. Incompressible Navier–Stokes equations, regularity of solu- tion, regularity criteria. 1. Introduction, main results We consider the Cauchy problem for the incompressible Navier–Stokes equa- tions, i.e. we look for the pair (u,p) satisfying ∂ t u − ν Δu +(u ·∇)u + ∇p = f , div u =0 (1.1) in the time-space cylinder (0,T ) × R 3 , together with the initial condition u(0, ·)= u 0 in R 3 . (1.2) For the sake of simplicity we put ν = 1 as its value does play any role in the present research of sufficient regularity conditions for weak solutions to be strong and unique.