scholarly journals Global existence and asymptotic convergence of weak solutions for the one-dimensional Navier–Stokes equations with capillarity and nonmonotonic pressure

2008 ◽  
Vol 245 (12) ◽  
pp. 3936-3955 ◽  
Author(s):  
Eugene Tsyganov
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Asymptotic Convergence ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One

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.

STATIONARY WEAK SOLUTIONS FOR STOCHASTIC 3D NAVIER–STOKES EQUATIONS WITH LÉVY NOISE

2012 ◽  
Vol 12 (01) ◽  
pp. 1150006 ◽  
Author(s):  
ZHAO DONG ◽  
WENBO V. LI ◽  
JIANLIANG ZHAI
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Probability Measures ◽  
Stationary Probability ◽  
Navier Stokes Equations ◽  
Wiener Processes ◽  
The One ◽  
Levy Noise

We first study the existence of stationary weak solutions of stochastic 3D Navier–Stokes equations involving jumps, and the associated Galerkin stationary probability measures for this case. Then we present a comparison between the Galerkin stationary probability measures for the case driven by Lévy noise and the one driven by Wiener processes.

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