Sums of large global solutions to the incompressible Navier-Stokes equations

2010/02/25 by Jean-Yves Chemin, Isabelle Gallagher, Chemin, Jean-Yves +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1002.4736

Accepted for publication in Journal für die reine und angewandte Mathematik

openalex publication_date 2010/02/25 · arxiv created 2010/10/01 · arxiv updated 2010/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be the (open) set of~ H^{\frac 1 2} divergence free vector fields generating a global smooth solution to the three dimensional incompressible Navier-Stokes equations. We prove that any element of G can be perturbed by an arbitrarily large, smooth divergence free vector field which varies slowly in one direction, and the resulting vector field (which remains arbitrarily large) is an element of G if the variation is slow enough. This result implies that through any point in G passes an uncountable number of arbitrarily long segments included in G.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

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