Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations

2019/06/29 by Bradshaw, Zachary, Tsai, Tai-Peng · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.00256

Abstract

This paper addresses several problems associated to local energy solutions (in the sense of Lemarié-Rieusset) to the Navier-Stokes equations with initial data which is sufficiently small at large or small scales as measured using truncated Morrey-type quantities, namely: (1) global existence for a class of data including the critical L²-based Morrey space; (2) initial and eventual regularity of local energy solutions to the Navier-Stokes equations with initial data sufficiently small at small or large scales; (3) small-large uniqueness of local energy solutions for data in the critical L²-based Morrey space. A number of interesting corollaries are included, including eventual regularity in familiar Lebesgue, Lorentz, and Morrey spaces, a new local generalized Von Wahl uniqueness criteria, as well as regularity and uniqueness for local energy solutions with small discretely self-similar data.

Cited by

• Time asymptotics, time regularity and separation rates for Navier-Stokes flows in supercritical solution classes
• The structure of weak solutions to the Navier-Stokes equations

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