Regularity of solutions to the Navier-Stokes equations evolving from\n small data in BMO^-1

2006/09/28 by Pierre Germain, Germain, Pierre, Nataša Pavlović +3 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0609781

openalex publication_date 2006/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2001, H. Koch and D. Tataru proved the existence of global in time\nsolutions to the incompressible Navier-Stokes equations in \ℝ^d for\ninitial data small enough in BMO^-1. We show in this article that the Koch\nand Tataru solution has higher regularity. As a consequence, we get a decay\nestimate in time for any space derivative, and space analyticity of the\nsolution. Also as an application of our regularity theorem, we prove a\nregularity result for self-similar solutions.\n

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• On the local Smoothness of Solutions of the Navier-Stokes Equations

Cited by

• Gevrey regularity solution for initial data in Triebel-Lizorkin-Lorentz spaces via single norm defined by nonlinearity of frequency

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