Global existence of large solutions to 3-D incompressible Navier-Stokes system

2024/06/26 by Ru, Shaolei
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.18308

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 B_∞,∞^-1, which contains all the known spaces in which there is a global solution for small data. In particular, this work extends the result of global well-posedness for the "ill-prepared" case in [6] to the full space ℝ³(in [6] the fluid evolves in domain \mathbbT²×ℝ)

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