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SIAM Journal on Mathematical Analysis, 2020
The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes equations through transport and buoyancy.
M. Winkler
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The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes equations through transport and buoyancy.
M. Winkler
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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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2013
In this chapter, we introduce a method of imposing asymmetric conditions on the velocity vector with respect to independent spatial variables and a moving-frame method to solve the three-dimensional Navier–Stokes equations. Seven families of unsteady rotating asymmetric solutions with various parameters are obtained.
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In this chapter, we introduce a method of imposing asymmetric conditions on the velocity vector with respect to independent spatial variables and a moving-frame method to solve the three-dimensional Navier–Stokes equations. Seven families of unsteady rotating asymmetric solutions with various parameters are obtained.
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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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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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2016
This chapter starts with two general principles: the mass and momentum conservations, valid for any fluid, complex or not, which will be used all along this book.
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This chapter starts with two general principles: the mass and momentum conservations, valid for any fluid, complex or not, which will be used all along this book.
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Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms
Springer Series in Computational Mathematics, 1986V. Girault, P. Raviart
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Incompressible Navier–Stokes Equations
2014We aim to derive the incompressible Navier–Stokes equations from classical mechanics. We define Lagrange and Euler coordinates and the mass density within the framework of measure theory. This yields a mathematical statement that expresses the mass conservation principle, which allows to derive the mass conservation equation.
Tomás Chacón Rebollo +1 more
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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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