Inflow Problem for the One-dimensional Compressible Navier-Stokes Equations under Large Initial Perturbation
arXiv:1403.1434 · doi:10.1016/j.jde.2014.07.001
Abstract
This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, Matsumura and Nishihara showed in [A. Matsumura and K. Nishihara, Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas. Comm. Math. Phys. 222 (2001), 449-474] that there exists boundary layer solution to the inflow problem and both the boundary layer solution, the rarefaction wave, and the superposition of boundary layer solution and rarefaction wave are nonlinear stable under small initial perturbation. The main purpose of this paper is to show that similar stability results for the boundary layer solution and the supersonic rarefaction wave still hold for a class of large initial perturbation which can allow the initial density to have large oscillation. The proofs are given by an elementary energy method and the key point is to deduce the desired lower and upper bounds on the density function.
24 pages
Cited by in corpus (9)
- Stability of stationary solutions to the outflow problem for full compressible Navier-Stokes equations with large initial perturbation
- Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space
- Existence and Nonlinear Stability of Steady-States to Outflow Problem for the Full Two-Phase Flow
- Asymptotic stability for the inflow problem of the heat-conductive ideal gas without viscosity
- Asymptotics of Radially Symmetric Solutions for the Exterior Problem of Multidimensional Burgers Equation
- Stability of degenerate stationary solution to the outflow problem for full Navier-Stokes equations
- Radially Symmetric Stationary Wave for Two-dimensional Burgers Equation
- Asymptotic stability of viscous contact wave and rarefaction waves for the system of heat-conductive ideal gas without viscosity
- Asymptotic stability of the rarefaction wave for the non-viscous and heat-conductive ideal gas in half space