Self-similar solutions to the Navier-Stokes equations: a survey of recent results

Abstract

We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].

25 pages, to appear in Harvard CMSA Series in Mathematics

References in corpus (4)

• Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces
• Fine properties of self-similar solutions of the Navier-Stokes equations
• Discretely self-similar solutions to the Navier-Stokes equations with Besov space data
• Existence of discretely self-similar solutions to the Navier-Stokes equations for initial value in $L_{loc}^2({\mathbb{R}}^3)$

Cited by in corpus (2)

• Charles Bouton and the Navier-Stokes Global Regularity Conjecture
• Time-Global Regularity of the Navier-Stokes System with Hyper-Dissipation--Turbulent Scenario