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On the generalized Navier–Stokes equations
Applied Mathematics and Computation, 2003In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.
El-Shahed, Moustafa, Salem, Ahmed
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A revisit of Navier–Stokes equation
European Journal of Mechanics - B/Fluids, 2020The authors studies the assumptions that serve as the base to derive the Navier-Stokes equation, focusing on the stress tensor and its symmetry. Along the history of the equation, its success, and challenges it is facing, the classical derivation is traced.
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Stochastic Navier-Stokes Equations
Acta Applicandae Mathematicae, 1995A survey of some results concerning the theory of stochastic Navier- Stokes equations is presented. The author gives a brief review of the deterministic theory of Navier-Stokes equations and then proves existence and uniqueness theorems for stochastic Navier-Stokes equations.
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On properties of the Navier–Stokes equations
Applied Mathematics and Computation, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2014
AbstractThis chapter concerns the statement and properties of the steady Navier–Stokes equations and the corresponding weak formulation. This includes discussion of stability theory, bifurcation and nonlinear iteration. This is followed by a description of finite element discretization and error analysis of discrete solutions.
Howard C. Elman +2 more
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AbstractThis chapter concerns the statement and properties of the steady Navier–Stokes equations and the corresponding weak formulation. This includes discussion of stability theory, bifurcation and nonlinear iteration. This is followed by a description of finite element discretization and error analysis of discrete solutions.
Howard C. Elman +2 more
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2005
Abstract The Navier-Stokes system is the basis for computational modeling of the flow of an incompressible Newtonian fluid, such as air or water.
Howard C Elman +2 more
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Abstract The Navier-Stokes system is the basis for computational modeling of the flow of an incompressible Newtonian fluid, such as air or water.
Howard C Elman +2 more
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1995
The methods of nonstandard analysis axe applied to the study of Navier-Stokes equations. We give a construction of weak solutions, solve general stochastic Navier-Stokes equations, and show how to obtain statistical solutions in the general stochastic case.
M. Capiński, N. J. Cutland
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The methods of nonstandard analysis axe applied to the study of Navier-Stokes equations. We give a construction of weak solutions, solve general stochastic Navier-Stokes equations, and show how to obtain statistical solutions in the general stochastic case.
M. Capiński, N. J. Cutland
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2020
The Navier-Stokes equations are a set of highly non-linear partial differential equations. We present these equations as the final example of partial differential equations, because of their special character and their importance in the field of fluid mechanics.
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The Navier-Stokes equations are a set of highly non-linear partial differential equations. We present these equations as the final example of partial differential equations, because of their special character and their importance in the field of fluid mechanics.
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TURBULENCE AND NAVIER-STOKES-EQUATIONS
1990This contribution reports on recent progress to explain fully developed, homogeneous, and isotropic turbulence of incompressible, single species fluid flow from the hydrodynamic equations. Only the main ideas are touched, for details the reader is referred to the original references. Various applications indicate the usefulness of the methods. There is
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2014
Navier-Stokes equations describe the motion of a fluid with constant density ρ in a domain Ω ⊂ ℝd (with d = 2,3). They read as follows $$\left\{ {\begin{array}{*{20}{l}} {\frac{{\partial {\mathbf{u}}}}{{\partial t}} - {\text{div}}[v(\nabla {\mathbf{u}} + \nabla {{\mathbf{u}}^T})] + ({\mathbf{u}}.\nabla ){\mathbf{u}} + \nabla {\mathbf{p}} = {\mathbf{
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Navier-Stokes equations describe the motion of a fluid with constant density ρ in a domain Ω ⊂ ℝd (with d = 2,3). They read as follows $$\left\{ {\begin{array}{*{20}{l}} {\frac{{\partial {\mathbf{u}}}}{{\partial t}} - {\text{div}}[v(\nabla {\mathbf{u}} + \nabla {{\mathbf{u}}^T})] + ({\mathbf{u}}.\nabla ){\mathbf{u}} + \nabla {\mathbf{p}} = {\mathbf{
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