Initial-boundary Value Problems to the One-dimensional Compressible Navier- Stokes-Poisson system with Large Amplitude

2016 ◽  
Vol 5 (2) ◽  
pp. 231-241
Author(s):  
Li Wang ◽  
Lei Jin
Keyword(s):  
Boundary Value Problems ◽  
Large Amplitude ◽  
Boundary Value ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Poisson System ◽  
One Dimensional ◽  
The One ◽  
Initial Boundary Value

Initial–boundary-value problems for one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients

2017 ◽  
Vol 147 (5) ◽  
pp. 935-969 ◽  
Author(s):  
Qing Chen ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Boundary Value Problems ◽  
Stokes Equations ◽  
Boundary Value ◽  
Transport Coefficients ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Initial Boundary Value

This paper is concerned with the construction of global, non-vacuum, strong, large amplitude solutions to initial–boundary-value problems for the one-dimensional compressible Navier–Stokes equations with degenerate transport coefficients. Our analysis derives the positive lower and upper bounds on the specific volume and the absolute temperature.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1356-1383
Author(s):  
Yong Wang ◽  
Wenpei Wu
Keyword(s):  
Equilibrium State ◽  
Boundary Value Problems ◽  
Electrostatic Potential ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Poisson Equations ◽  
Initial Boundary Value

Abstract We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H 2 space is obtained. Moreover, we prove that the solution decays to the equilibrium state at an exponential rate as time tends to infinity. This is the first result for the three-dimensional elastic Navier-Stokes-Poisson equations under various boundary conditions for the electrostatic potential.

Sign in / Sign up

Export Citation Format

Share Document