Unique solvability of a two-dimensional nonstationary problem for the convection equations with temperature-dependent viscosity
type: Item
instance of: scholarly article
title: Unique solvability of a two-dimensional nonstationary problem for the convection equations with temperature-dependent viscosity
zbMATH Open document ID: 1055.35090
DOI: 10.1023/A:1015337513832
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The global motion of a drop of a viscous compressible heat conducting fluid is considered. Assuming that the initial data are sufficiently close to an equilibrium state and the external force, the heat sources and the heat flow through the boundary vanish, the authors prove the existence of a global in time solution to the appropriate equations which is close to the equilibrium state for any moment of time. They rewrite the main equations in Lagrangian coordinates in order to formulate the local existence theorem, and apply the method of successive approximations to prove the local existence. To prove the global existence of the solutions, they obtain fine estimates and consider appropriate compatibility conditions on the boundary.
reviewed by: Mariano Rodríguez Ricard
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1916032
zbMATH Keywords: global existence
zbMATH Keywords: local existence
zbMATH Keywords: regularity
zbMATH Keywords: uniqueness
zbMATH Keywords: viscous compressible heat conducting fluid
author: Olga N. Goncharova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1916032