scholarly journals A rigorous derivation of the stationary compressible Reynolds equation via the Navier–Stokes equations

2018 ◽  
Vol 28 (04) ◽  
pp. 697-732 ◽  
Author(s):  
I. S. Ciuperca ◽  
E. Feireisl ◽  
M. Jai ◽  
A. Petrov
Keyword(s):  
Reynolds Equation ◽  
Stokes System ◽  
Stokes Equations ◽  
A Priori ◽  
Limit Problem ◽  
Navier Stokes ◽  
Rigorous Derivation ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier–Stokes system on a thin domain. In particular, the existence of solutions to the Navier–Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the one-dimensional case.

INTRODUCING OF INTERNAL VISCOUS FRICTION IN EQUATIONS OF BEAM OSCILLATION AS LONG RECTANGULAR STRIP

2021 ◽  
pp. 54-58
Author(s):  
E.M. Zveriaev ◽  
Keyword(s):  
Stokes Equations ◽  
Asymptotic Series ◽  
Viscous Friction ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Dimensional Theory ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Beam Oscillation

Abstract. On the base of the method of simple iterations generalising methods of semi-inverse one of Saint-Venant, Reissner and Timoshenko the one-dimensional theory is constructed using the example of dynamic equations of a plane problem of elasticity theory for a long elastic strip. The resolving equation of that one-dimensional theory coincides with the equation of beam vibrations. The other problems with unknowns are determined without integration by direct calculations. In the initial equations of the theory of elasticity the terms corresponding to the viscous friction in the Navier-Stokes equations are introduced. The asymptotic characteristics of the unknowns obtained by the method of simple iterations allow to search for a solution in the form of expansions of the unknowns into asymptotic series. The resolving equation contains a term that depends on the coefficient of viscous friction.

Cauchy problem for the one-dimensional compressible Navier-Stokes equations

2012 ◽  
Vol 32 (1) ◽  
pp. 315-324 ◽  
Author(s):  
Lian Ruxu ◽  
Liu Jian ◽  
Li Hailiang ◽  
Xiao Ling
Keyword(s):  
Cauchy Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One
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