On the spatially asymptotic structure of time-periodic solutions to the\n Navier-Stokes equations

2020/05/27 by Thomas Eiter, Eiter, Thomas
Computer Science · Engineering · Mathematics · #35B10 #35C20 #35E05 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Primary 35Q30 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2005.13268

openalex publication_date 2020/05/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

The asymptotic behavior of weak time-periodic solutions to the Navier-Stokes\nequations with a drift term in the three-dimensional whole space is\ninvestigated. The velocity field is decomposed into a time-independent and a\nremaining part, and separate asymptotic expansions are derived for both parts\nand their gradients. One observes that the behavior at spatial infinity is\ndetermined by the corresponding Oseen fundamental solutions.\n

Related

• Time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space with a non-zero drift term: Asymptotic profile at spatial infinity
• Asymptotic expansions with subordinate variables for solutions of the Navier-Stokes equations
• Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body forces
• Spatial decay/asymptotics in the Navier-Stokes equation
• The Navier-Stokes equations with body forces decaying coherently in time