Existence of solutions to a model for sparse, one-dimensional fluids
type: Item
instance of: scholarly article
title: Existence of solutions to a model for sparse, one-dimensional fluids
zbMATH Open document ID: 1214.35045
author: David Hoff
published in: Journal of Differential Equations
publication date: 2011-01-18T00:00:00Z
review text: A model for a viscous, compressible, barotropic fluid initially occupying a general open subset of a finite, one-dimensional interval is considered. The author introduce a notation of weak solution which insures that the momentum of a fluid packet isolated from the spatial boundary on some time interval is conserved on that time interval. Then by tracking the fluid set and accommodate the possibly infinite number of collisions of fluid packets occurring on a possibly dense set of collision times, the author constructed a globally-locally momentum-conserving weak solution. The author's arguments can avoid some nonphysical properties of solutions resulting from the insertion of artificial mass.
reviewed by: Cheng He
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 5838460
zbMATH Keywords: compressible Navier-Stokes equations
zbMATH Keywords: weak solutions
zbMATH Keywords: local momentum conservation
MaRDI profile type: Publication
full work available at URL: j.jde.2010.09.010
OpenAlex ID: W2045270447
cites work: Compressible Navier–Stokes equations with vacuum state in the case of general pressure law
cites work: Q5702675
cites work: Global existence and asymptotic behavior of weak solutions to the 1D compressible Navier–Stokes equations with degenerate viscosity coefficient
cites work: Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data
cites work: Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data
cites work: Compressible flow in a half-space with Navier boundary conditions
cites work: The Failure of Continuous Dependence on Initial data for the Navier–Stokes equations of Compressible Flow
cites work: Time analyticity and backward uniqueness of weak solutions of the Navier-Stokes equations of multidimensional compressible flow
cites work: Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity
cites work: Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting, one-dimensional real gas
cites work: Q3142937
cites work: Vacuum states for compressible flow
cites work: Interface Behavior of Compressible Navier--Stokes Equations with Vacuum
cites work: Q4707325
cites work: Global existence of solutions for compressible Navier-Stokes equations with vacuum
cites work: Q3731278
cites work: Global properties of solutions to 1D-viscous compressible barotropic fluid equations with density dependent viscosity
cites work: On the global solution and interface behaviour of viscous compressible real flow with free boundaries
cites work: Global solutions of the Navier-Stokes equations for viscous compressible flows.
cites work: A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
cites work: COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY AND VACUUM
DOI: 10.1016/J.JDE.2010.09.010
description: scientific article; zbMATH DE number 5838460