Global existence of large solutions to 3-D incompressible Navier-Stokes system (2406.18308v1)

Abstract: This paper proves that the 3-D Navier-Stokes system has a unique global solution under an assumpution on the initial data. That allow the data to be arbitrarily large in the scale invariant space \dot{B}_{\infty,\infty}^{-1}, which contains all the known spaces in which there is a global solution for small data. Moreover, this result provides various examples of arbitrarily large initial data giving rise to global solutions.