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On a theorem by Sohr for the Navier-Stokes equations
Journal of Evolution Equations, 2004The authors study some criteria for the full (space-time) regularity of weak solutions to the Navier-Stokes equations. In particular, some classical and very recent criteria involving the velocity, or its derivates are generalized. More spoecifically, it is shown with elementary tools that if a weak solution, or its vorticity, is small in appropriate ...
BERSELLI, LUIGI CARLO, MANFRIN R.
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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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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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2019
The dynamics of the Newtonian fluids considered here are determined by the laws of classical mechanics, a selection of references for the derivation of the fundamental pdes from these laws are Lamb [1], Landau and Lifshitz [2], Serrin [3], Majda and Bertozzi [4], Wu et al. [5].
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The dynamics of the Newtonian fluids considered here are determined by the laws of classical mechanics, a selection of references for the derivation of the fundamental pdes from these laws are Lamb [1], Landau and Lifshitz [2], Serrin [3], Majda and Bertozzi [4], Wu et al. [5].
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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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Stokes and Navier-Stokes equations with Navier boundary conditions
Journal of Differential Equations, 2021Carlos Conca, C Amrouche
exaly
1990
Abstract The resistance arising from the want of lubricity in the parts of a fluid is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another.
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Abstract The resistance arising from the want of lubricity in the parts of a fluid is, other things being equal, proportional to the velocity with which the parts of the fluid are separated from one another.
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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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