Continuum and discrete hydrodynamical models and globally well-posed problems
type: Item
instance of: scholarly article
title: Continuum and discrete hydrodynamical models and globally well-posed problems
zbMATH Open document ID: 0652.76002
DOI: 10.1016/0096-3003(88)90126-9
author: K. L. Kuttler
author: Darrell L. Hicks
published in: Applied Mathematics and Computation
publication date: 1988-01-01T00:00:00Z
review text: Two models for one-dimensional hydrodynamical motion are model C and model D. Model C is the standard, classical, continuum model. Well- posedness proofs for problems based on model C encounter extreme technical difficulties. There are dubious steps in the derivation of model C from first principles. Model D is a modification of model C which avoids these dubious steps. A mixed, initial-boundary-value problem based on model D is properly posed globally. The proof presented here is for the pressure obeying a generalization of the ideal-gas law and a viscous stress obeying a generalization of the Navier-Stokes form. No assumptions requiring the initial data to be small deviations from a constant state are required; the initial data are only required to be physically acceptable.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 82D15
zbMATH DE Number: 4064623
zbMATH Keywords: one-dimensional hydrodynamical motion
zbMATH Keywords: standard, classical, continuum model
zbMATH Keywords: Well-posedness proofs
zbMATH Keywords: mixed, initial-boundary-value problem
zbMATH Keywords: generalization of the ideal-gas law
zbMATH Keywords: generalization of the Navier-Stokes form
MaRDI profile type: Publication
full work available at URL: 0096-3003(88)90126-9
OpenAlex ID: W1975928654
Wikidata QID: Q126340335
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description: scientific article; zbMATH DE number 4064623