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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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2014
The main goal of this chapter is to present the Navier-Stokes equation, both for incompressible and compressible fluids. The equation is written in the cartesian tensor notation and also in the usual vector form. The viscosity and rate of strain tensors are introduced, as well as the viscosity coefficients.
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The main goal of this chapter is to present the Navier-Stokes equation, both for incompressible and compressible fluids. The equation is written in the cartesian tensor notation and also in the usual vector form. The viscosity and rate of strain tensors are introduced, as well as the viscosity coefficients.
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2013
As mentioned in the introduction, the Navier-Stokes equations constitute the conservation of mass and momentum for incompressible Newtonian fluids. Of course, these basic equations of fluid dynamics as well as their derivation can be found in many popular and classical books, see e. g. [Lam32] or [Bat00].
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As mentioned in the introduction, the Navier-Stokes equations constitute the conservation of mass and momentum for incompressible Newtonian fluids. Of course, these basic equations of fluid dynamics as well as their derivation can be found in many popular and classical books, see e. g. [Lam32] or [Bat00].
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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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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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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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Solving integral equations in free space with inverse-designed ultrathin optical metagratings
Nature Nanotechnology, 2023Andrea Cordaro, Andrea Alu
exaly
DeepXDE: A Deep Learning Library for Solving Differential Equations
SIAM Review, 2021Lu Lu, George E Karniadakis
exaly