A model of stochastic differential equation in Hilbert applicable to Navier-Stokes equation in dimension 2

1990 ◽  
Author(s):  
A. Bensoussan
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dimension 2

scholarly journals Solusi Persamaan Burgers Inviscid dengan Metode Pemisahan Variabel

2021 ◽  
Vol 4 (2) ◽  
pp. 88
Author(s):  
Hisyam Ihsan ◽  
Syafruddin Side ◽  
Muhammad Iqbal
Keyword(s):  
Differential Equation ◽  
Stokes Equation ◽  
Burgers Equation ◽  
Equation System ◽  
Separation Method ◽  
Navier Stokes ◽  
Variable Separation ◽  
Partial Differential ◽  
Navier Stokes Equation ◽  
Variable Separation Method

Penelitian ini mengkaji tentang solusi persamaan Burgers Inviscid dengan metode pemisahan variabel. Tujuan dari penelitian ini adalah untuk mengetahui penyederhanaan sistem persamaan Navier-Stokes menjadi persamaan Burgers Inviscid, menemukan solusi persamaan Burgers Inviscid dengan metode pemisahan variabel, dan melakukan simulasi solusi persamaan dengan menggunakan software Maple18. Persamaan Burgers muncul sebagai penyederhanaan model yang rumit dari sistem persamaan Navier-Stokes. Persamaan Burgers adalah persamaan diferensial parsial hukum konservasi dan merupakan masalah hiperbolik, yaitu representasi nonlinier paling sederhana dari persamaan Navier-Stokes. Metode pemisahan variabel merupakan salah satu metode klasik yang efektif digunakan dalam menyelesaikan persamaan diferensial parsial dengan mengasumsikan  untuk mendapatkan komponen x dan t. Kemudian akan dilakukan subtitusi pada persamaan diferensial, sehingga dengan cara ini akan didapatkan solusi persamaan diferensial parsial.Kata Kunci: Persamaan Burgers Inviscid, metode pemisahan variabel, persamaan Navier-StokesThis study examines the solution of Burgers Inviscid equation with variable separation method. The purpose of this study was to find out the simplification of the Navier-Stokes equation system into the Burgers Inviscid equation, find a solution to the Burgers Inviscid equation with the variable separation method, and simulate equation solutions using Maple18 software. The Burgers equation emerged as a complicated simplification of the Navier-Stokes equation system. The Burgers equation is a partial differential equation of conservation law and is a hyperbolic problem, i.e. the simplest nonlinear representation of the Navier-Stokes equation. The variable separation method is one of the classic methods that is effectively used in solving partial differential equations assuming  to obtain the x and t components. Then there will be substitutions to differential equations, so that in this way there will be a partial differential equation solution.Keywords: Burgers Inviscid Equation, variable separation method, Navier-Stokes equations.

scholarly journals Conservation of Total Vorticity for a 2D Stochastic Navier Stokes Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Peter M. Kotelenez ◽  
Bradley T. Seadler
Keyword(s):  
Differential Equation ◽  
Stokes Equation ◽  
Continuum Limit ◽  
Empirical Process ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Spatially Correlated ◽  
State Dependent ◽  
Point Measure ◽  
Stochastic Term

We consider point vortices whose positions satisfy a stochastic ordinary differential equation on perturbed by spatially correlated Brownian noise. The associated signed point measure-valued empirical process turns out to be a weak solution to a stochastic Navier-Stokes equation (SNSE) with a state-dependent stochastic term. As the number of vortices tends to infinity, we obtain a smooth solution to the SNSE, and we prove the conservation of total vorticity in this continuum limit.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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