Physically reasonable solutions to steady compressible Navier-Stokes equations in 3D exterior domains \((v_ \infty\neq 0)\)
type: Item
instance of: scholarly article
title: Physically reasonable solutions to steady compressible Navier-Stokes equations in 3D exterior domains \((v_ \infty\neq 0)\)
zbMATH Open document ID: 0883.76072
author: Antonín Novotný
author: Mariarosaria Padula
published in: Mathematische Annalen
publication date: 1998-03-23T00:00:00Z
review text: We consider steady compressible Navier-Stokes equations in barotropic, isentropic or isothermal regime in three-dimensional exterior domains with the velocity at infinity equal to a strictly nonzero constant vector. Under the assumptions on the smallness of the external force and of the prescribed velocity at infinity, we prove existence and uniqueness of solutions, in the class of functions possessing the same pointwise decay as the fundamental Oseen tensor. In particular, we prove existence of the wake region, where the velocity and its gradients decay more slowly then outside it; the decay rate corresponds to that one of the Oseen equation. In this sense, the result is optimal. Further, the (singular) limit when the velocity at infinity tends to zero, is investigated. The main tool in the proof is the method of decomposition.
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1057248
zbMATH Keywords: singular limit
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: fundamental Oseen tensor
zbMATH Keywords: wake region
zbMATH Keywords: method of decomposition
MaRDI profile type: Publication
full work available at URL: s002080050084
OpenAlex ID: W2024450899
DOI: 10.1007/S002080050084
description: scientific article; zbMATH DE number 1057248