Large-time behavior and far field asymptotics of solutions to the Navier-Stokes equations

2018/04/05 by Masakazu Yamamoto, Yamamoto, Masakazu
Engineering · Mathematics · #35B40 #35C20 #35Q30 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1804.01746

openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Asymptotic expansions of global solutions to the incompressible Navier-Stokes equation as t tends to infinity with high-order is studied and large-time behavior of the expansion is clarified. Furthermore, far field asymptotics also is derived. Those expansions are provided without moment conditions on the initial velocity. The Biot-Savard law together with the renormalization for the vorticity equations yields those expansions.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• Sur le mouvement d'un liquide visqueux emplissant l'espace

Related

• Time evolution of the Navier-Stokes flow in far-field
• High Order Asymptotic Expansion at Infinity for Strong Solutions to Incompressible Navier-Stokes Equations
• Fine large-time asymptotics for the axisymmetric Navier--Stokes equations
• Spatial asymptotic expansions in the Navier-Stokes equation
• Large, global solutions to the Navier-Stokes equations, slowly varying in one direction