Classical Fundamental Unique Solution for the Incompressible Navier-Stokes Equation in R&amp;lt;sup&amp;gt;&amp;lt;i&amp;gt;N&amp;lt;/i&amp;gt;&amp;lt;/sup&amp;gt;

Khedr, Waleed S.

doi:10.4236/jamp.2017.54083

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…It remains to answer the question whether there exists another possible solution to Model Equation (5) in the sense of Definition 2.1. The orthogonality argument presented in [KW,Theorem 4] to prove uniqueness remains valid in the context of this article. It simply depends on the coincidence of any possible solutions on the boundary.…”

Section: Resultsmentioning

confidence: 84%

Nonconvection and uniqueness in Navier-Stokes equation

Khedr

2017

Preprint

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In the presence of a certain class of functions we show that there exists a smooth solution to Navier-Stokes equation. This solution entertains the property of being nonconvective. We introduce a definition for any possible solution to the problem with minimum assumptions on the existence and the regularity of such solution. Then we prove that the proposed class of functions represents the unique solution to the problem and consequently we conclude that there exists no convective solutions to the problem in the sense of the given definition. Contents 1. Introduction 1 2. Statement of the problem 3 3. Main results 4 4. Conclusions 9 References 9

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Section: Resultsmentioning

confidence: 84%

Nonconvection and uniqueness in Navier-Stokes equation

Khedr

2017

Preprint

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Computational analysis of multi-layered Navier–Stokes system by Atangana–Baleanu derivative

Alqahtani,

Shukla

2023

Applied Mathematics in Science and Engineering

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Analyzing the influence of a particle's linear and angular velocity on the equations of liquid motion

Budarin

2021

EEJET

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This paper has analyzed the equation of motion in terms of stresses (Navier), as well as its two special cases for an incompressible viscous current. One is the Stokes (Navier-Stokes) equation, and the other was derived with fewer restrictions. It has been shown that the Laplace equation of linear velocity can be represented as a function of two variables ‒ the linear and angular speed of particle rotation. To describe the particle acceleration, all motion equations employed a complete derivative from speed in the Gromeka-Lamb form, which depends on the same variables. Taking into consideration the joint influence of linear and angular velocity allows solving a task of the analytical description of a turbulent current within the average model. A given method of analysis applies the provision of general physics that examines the translational and rotational motion. The third type of mechanical movement, oscillatory (pulsation), was not considered in the current work. A property related to the Stokes equation decomposition has been found; a block diagram composed of equations and conditions has been built. It is shown that all equations for viscous liquid have their own analog in a simpler model of non-viscous fluid. That makes it easier to find solutions to the equations for the viscous flow. The Stokes and Navier equations were used to solve two one-dimensional problems, which found the distribution of speed along the normal to the surface at the flow on a horizontal plate and in a circular pipe. Both solution methods produce the same result. No solution for the distribution of speed along the normal to the surface in a laminar sublayer could be found. A relevant task related to the mathematical part is to solve the problem of closing the equations considered. A comparison of the theoretical and empirical equations has been performed, which has made it possible to justify the assumption that a rarefied gas is the Stokes liquid

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Classical Fundamental Unique Solution for the Incompressible Navier-Stokes Equation in R<sup><i>N</i></sup>

Cited by 3 publications

References 16 publications

Nonconvection and uniqueness in Navier-Stokes equation

Nonconvection and uniqueness in Navier-Stokes equation

Computational analysis of multi-layered Navier–Stokes system by Atangana–Baleanu derivative

Analyzing the influence of a particle's linear and angular velocity on the equations of liquid motion

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