NAVIER-STOKES EQUATIONS IN THE BESOV SPACE NEAR L^∞ AND BMO

Abstract

We prove a local existence theorem for the Navier-Stokes equations with the initial data in B⁰_∞,∞ containing functions which do not decay at infinity. Then we establish an extension criterion on our local solutions in terms of the vorticity in the homogeneous Besov space B^·0_∞,∞.