On singular limit equations for incompressible fluids in moving thin domains

2017/03/28 by Tatsu‐Hiko Miura, Miura, Tatsu-Hiko · 1 citation
Computer Science · Engineering · Mathematics · #35Q35 #35R01 #76A20 #76M45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.09698

openalex publication_date 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-dimensional moving closed surface as the width of the thin domain goes to zero, we give a heuristic derivation of singular limit equations on the degenerate moving surface of the Euler and Navier-Stokes equations in the moving thin domain and investigate relations between their energy structures. We also compare the limit equations with the Euler and Navier-Stokes equations on a stationary manifold, which are described in terms of the Levi-Civita connection.

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