Solvability of nonstationary problems for nonhomogeneous incompressible fluids and the convergence with vanishing viscosity
type: Item
instance of: scholarly article
title: Solvability of nonstationary problems for nonhomogeneous incompressible fluids and the convergence with vanishing viscosity
zbMATH Open document ID: 0943.35075
author: Shigeharu Itoh
author: Atusi Tani
published in: Tokyo Journal of Mathematics
publication date: 2000-09-06T00:00:00Z
review text: A ``hybrid'' system is considered, formed by a Navier-Stokes type equation, the divergence free condition for ``velocity'' and an evolution equation for ``density''. The main point is to study the above system as function of the ``viscosity''. The Cauchy problem is studied with corresponding boundary conditions, in the cases of non-zero and vanishing ``viscosity''. A unicity and existence theorem is given for the two above cases. An interesting theorem is proved, concerning the convergence of the solution when the ``viscosity'' tends to zero. To prove this result, an approximate solution is constructed inductively and ``a priori'' estimates are given.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 1340485
zbMATH Keywords: convergence for vanishing viscosity
zbMATH Keywords: evolution equation for density
zbMATH Keywords: a priori estimates
zbMATH Keywords: Navier-Stokes type equation
zbMATH Keywords: unicity
zbMATH Keywords: existence
zbMATH Keywords: approximate solution
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270041610
OpenAlex ID: W2026992469
DOI: 10.3836/TJM/1270041610
description: scientific article; zbMATH DE number 1340485