Inertial Forms of Navier-Stokes Equations on Sphere

1993/04/14 by Roger Témam, Temam, Roger, Shouhong Wang +1 · 1 citation
Engineering · Mathematics · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.chao-dyn/9304004

openalex publication_date 1993/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we derive an upper bound on the dimension of the differential system (inertial manifold) which fully reproduces the infinite dimensional dynamics. This bound is expressed in terms of Grashof Numbers.

Cited by

• Difference estimate for weak solutions to the Navier-Stokes equations in a thin spherical shell and on the unit sphere

Related

• Navier-Stokes equations, determining forms, determining modes, inertial manifolds, dissipative dynamical systems
• Inertial manifolds for the incompressible Navier-Stokes equations
• Manifold Solutions to Navier-Stokes Equations
• Exact solutions of fluid equations on a sphere
• K"ahler Geometry and the Navier-Stokes Equations