scholarly journals On the solvability of boundary and initial-boundary value problems for the Navier-Stokes system in domains with noncompact boundaries

1981 ◽  
Vol 93 (2) ◽  
pp. 443-458 ◽  
Author(s):  
Vsevolod Solonnikov
Keyword(s):  
Boundary Value Problems ◽  
Stokes System ◽  
Boundary Value ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

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.

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.

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