On Global Infinite Energy Solutions¶to the Navier-Stokes Equations¶in Two Dimensions

Abstract

This paper studies the bidimensional Navier–Stokes equations with large initial data in the homogeneous Besov space . As long as r,q < +∞, global existence and uniqueness of solutions are proved. We also prove that weak–strong uniqueness holds for the d-dimensional equations with data in L 2(ℝ d ) for d/r+ 2/q≥ 1.