Global solutions of a high dimensional system for Korteweg materials
type: Item
instance of: scholarly article
title: Global solutions of a high dimensional system for Korteweg materials
zbMATH Open document ID: 0858.35124
author: H. H. Harumi Hattori
author: Dening Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-03-23T00:00:00Z
review text: The main goal of this paper is to study the system for isothermal motion of Korteweg type: \[ \rho_t+(\rho u)_x+(\rho v)_y=0, \] \[ (\rho u)_t+(\rho u^2)_x+(\rho uv)_y= -\rho_x+\nu \rho\Delta\rho_x+ \mu\Delta u+(\mu/3)(u_{xx}+v_{xy}), \] \[ (\rho v)_t+(\rho uv)_x+ (\rho v^2)_y=-\rho_y+ \nu\rho\Delta\rho_y+ \mu\Delta v+(\mu/3)(u_{xy}+v_{yy}) \] with initial data \((\rho,u,v)(x,y,0)= (\rho_0,u_0,v_0)(x,y)\). The authors extend some known results, establish the global existence of the solution, and give necessary adjustments for the general high-dimensional case.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 902488
zbMATH Keywords: isothermal motion of Korteweg type
zbMATH Keywords: global existence
zbMATH Keywords: high-dimensional case
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0069
OpenAlex ID: W2046249983
DOI: 10.1006/JMAA.1996.0069
description: scientific article; zbMATH DE number 902488