Global solutions to 3D incompressible Navier-Stokes equations with some large initial data

In this paper, we derive a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations. More precisely, we prove that if (parallel to u(0)(1) + u(0)(2)parallel to(3/p-1)(<(B) over dot>)(p,1) + parallel to u(0)(3)parallel to(3/p-1)(<(B) over dot>)(p,1)) x exp(C(parallel to u(0)parallel to(2)(-1)(<(B) over dot>)(infinity,1) + parallel to u(0)parallel to(-1)(<(B) over dot>)(infinity,1))) is small enough, the Navier-Stokes equations have a unique global solution. As an application, we construct two examples of initial data satisfying the smallness condition, but whose (-1)((B) over dot>)(infinity,infinity)(R-3) norm can be arbitrarily large. (C) 2022 Elsevier Ltd. All rights reserved.