Global weak Besov solutions of the Navier-Stokes equations and applications

Tobias Barker, Dallas Albritton

Research output: Contribution to journalArticlepeer-review

15 Citations (SciVal)

Abstract

We introduce a notion of global weak solution to the Navier–Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces B˙−1+3pp,∞, p > 3. These solutions satisfy a certain stability property with respect to the weak-∗ convergence of initial conditions. To illustrate this property, we provide applications to blow-up criteria, minimal blow-up initial data, and forward self-similar solutions. Our proof relies on a new splitting result in homogeneous Besov spaces that may be of independent interest.
Original languageEnglish
Pages (from-to)197–263
JournalArchive for Rational Mechanics and Analysis
Volume232
DOIs
Publication statusPublished - 9 Oct 2018

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