Global NavierStokes flows for nondecaying initial data with slowly decaying oscillation
Abstract
Consider the Cauchy problem of incompressible NavierStokes equations in $\mathbb{R}^3$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the existence of a timeglobal weak solution has been known. However, such data do not include constants, and the only known global solutions for nondecaying data are either for perturbations of constants, or when the velocity gradients are in $L^p$ with finite $p$. In this paper, we construct global weak solutions for nondecaying initial data whose local oscillations decay, no matter how slowly.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.03249
 Bibcode:
 2018arXiv181103249K
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 We added reference to LemarieRieusset [21] on page 2, Example 1.2 after Theorem 1.1, and Theorem 6.1 in a new Section 6 of 2 pages. This version is accepted by the Communications in Mathematical Physics