Interface Behavior of Compressible Navier--Stokes Equations with Vacuum
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 31 (6) , 1175-1191
- https://doi.org/10.1137/s0036141097331044
Abstract
In this paper, we study a one-dimensional motion of viscous gas near vacuum with (or without) gravity. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier--Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes continuously. The regularity and behavior of the solutions near the interfaces and expanding rate of the interfaces are studied. Smoothness of the solutions is discussed. The uniqueness of the weak solutions to the free boundary problem is also proved.Keywords
This publication has 11 references indexed in Scilit:
- Blowup of smooth solutions to the compressible Navier‐Stokes equation with compact densityCommunications on Pure and Applied Mathematics, 1998
- Vacuum states for compressible flowDiscrete & Continuous Dynamical Systems, 1998
- Free boundary problem for the equation of spherically symmetric motion of viscous gas (II)Japan Journal of Industrial and Applied Mathematics, 1995
- Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial dataArchive for Rational Mechanics and Analysis, 1995
- Free boundary problem for the equation of spherically symmetric motion of viscous gasJapan Journal of Industrial and Applied Mathematics, 1993
- The Failure of Continuous Dependence on Initial data for the Navier–Stokes equations of Compressible FlowSIAM Journal on Applied Mathematics, 1991
- Free boundary value problems for the equation of one-dimensional motion of viscous gasJapan Journal of Applied Mathematics, 1989
- Equations of fluid dynamics—free surface problemsCommunications on Pure and Applied Mathematics, 1986
- Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial dataProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1986
- Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gasesKyoto Journal of Mathematics, 1981