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0answers
103 views

Reference request: has this semilinear version of Navier Stokes been studied?

I have noticed that the Navier Stokes equations can be written as a semilinear symmetric first order system $$ u_t+A_1u_{x_1}+A_2u_{x_2}+A_3u_{x_3} = f(u) $$ for a 9 by 1 vector $u$ containing the ...
2
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0answers
74 views

Is a certain set of periodic solutions of the 2D Navier-Stokes equations closed generically?

I would be interested to know if a certain set of periodic solutions for the two-dimensional Navier-Stokes equations is closed generically. Many similar (yet not identical) set-ups can be found in the ...
12
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0answers
5k views

Otelbayev's approach to Navier-Stokes [closed]

Recent news post that Mukhtarbai Otelbayev from Eurasian National University has shown existence of strong solutions of the Navier-Stokes equation in the article "Existence of a strong solution of ...
2
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0answers
166 views

Looking for good conferences / workshops on applications of renormalization group methods [closed]

I am looking for conferences and/or workshops, where people working on different problems using renormalization group methods come together to share their results and experience. As I have noted, ...
3
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0answers
83 views

What does the renormalization group flow corresponding to a turbulent subrange with a broad band forcing look like?

In a renormalization group analysis of turbulent flows, such as for example done by Barbi and Münster here who derive an action for the Navier-Stokes equations, insert it into the Wilson equation, and ...
4
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1answer
176 views

Doubt on Morrey spaces of measures according to T. Giga and Y. Miyakawa

I'm reading 'Navier-Stokes flow in $\mathbb{R}^3$ with measures as initial vorticity and Morrey spaces' (a paper of Giga and Miyakawa) but there is something that I don't understand about the ...
1
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1answer
206 views

Reference request: Spectral analysis of advection diffusion PDE

As the title says, I am looking for a authoritative reference/monograph on this topic. My interest is in spectral properties of this PDE, and NOT on existence/uniqueness etc. which is usually the ...
2
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0answers
103 views

A question on discrete numerical simulation on fluids mechanics

I read the paper "Stable, circulation-preseving simplicial fuids" by Elcott, et al: http://www.cs.jhu.edu/~misha/Fall09/Elcott07.pdf. It gives a structure preseving discretization of fluids. I have ...
3
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0answers
102 views

What is the relationship between complex time singularities and UV fixed points?

In this paper it is described how the turbulent kinetic energy spectrum and the flatness (a measure for intermittency) are governed by the position of the (dominant) singularities of the solutions of ...
10
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1answer
270 views

Do circular pipes maximize flow rate?

Suppose that $U \subset \mathbb{R}^2$ is nonempty, open, connected and bounded. Consider a Poisseuille flow in the pipe $U \times \mathbb{R}$. That is: a time-independent incompressible flow of the ...
2
votes
1answer
132 views

First integrals of a 3D incompressible flow

Let $\Omega$ be an unbounded periodic smooth domain of $\mathbb{R}^3$. We are Given an incompressible vector field $q:\Omega\subset\mathbb{R}^3\rightarrow \mathbb{R}^3$ (i.e. $\nabla\cdot q\equiv 0$ ...
2
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1answer
471 views

Derivation of Bessel functions

I am writing a summary on a work on Fluid Dynamics that develops irrotational flow states that appear to interact amongst each other according to the equations of Electromagnetism ...
3
votes
1answer
106 views

The discrete theory of compressible fluids dynamics

I am working on the discrete theory of compressible fluids dynamics, i.e., numerically solving and simulating the compressible fluids , we are interested in the way using discrete exterior calculus, ...
5
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0answers
134 views

Constructing black noise with non-standard analysis

With noise in the sense of i.i.d. random sequence, a noise is black if it is not isomorphic to standard Gaussian white noise. Tsirelson showed the existence of black noise through the scaling limit ...
1
vote
1answer
280 views

Solving Stokes Equations using 3D Fourier transforms

How do you calculate the inverse Fourier transform of $\frac{k_ik_j}{k^4}$. I know it has to be a matrix of the form $=δ_{ij}A(r)+r_ir_jB(r)$, but how do you calculate the functions A(r) and B(r)? I ...
0
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3answers
342 views

problem related to Airy functions [closed]

I have solved the Schrödinger equation for a triangular well potential and the solution comes in terms of Airy functions...now i am facing the following problems: What are the normalization ...
0
votes
1answer
197 views

Inequality between gradient and divergent

Consider functions v:R^d->R^d (d is dimension 2 or 3 and v is a velocity field) and v in X=H_0^1 (Sobolev space). I would like to prove the inequality ||div(v)||_X <= ...
9
votes
2answers
671 views

Convergence of solutions to Navier-Stokes to Euler's equation for viscosity $\to$ zero

Let $$ \partial_t u + \nabla_u u = - \nabla p $$ be Euler's equation (Wikipedia) for an ideal incompressible fluid. Let $$ \partial_t u + \nabla_u u - \nu \Delta u = - \nabla p $$ be the ...
2
votes
0answers
230 views

Monge Ampere and Calculus

[ I posted the question on Math StackExchange but didn't get any reply nor comment, so I'm trying here ] I am learning about mass transportation theory and the Monge-Ampere equation, to transport a ...
1
vote
0answers
169 views

Velocity field of fluid and Maurer-Cartan form?

Chatting with an engineer, he suggested me to have a look to a certain book in order to understand what fluid mechanics is about (I know nothing about the subject). But this question is not about ...
5
votes
1answer
354 views

A moving boundary in rock mechanics

I'm concern a moving boundary problem in rock mechanics. We consider a problem of unsaturated flow of an in-compressible fluid in a porous medium(rock) like D. Moreover suppose that support of a ...
4
votes
2answers
591 views

Vortex Voronoi diagram?

Suppose there are a finite number of disjoint unit-radii disks in the plane, each spinning clockwise or counterclockwise at the same angular velocity. The plane is filled with a thin fluid layer, and ...
2
votes
0answers
209 views

Why is a smooth weak solution strong for stationary linear Stokes problem with zero-traction boundary condition?

Can anyone provide me with a reference giving details on how smooth generalized solutions of the stationary linear Stokes problem can be shown to be classical solutions when a zero-traction boundary ...
21
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5answers
2k views

Is there a mathematically precise definition of turbulence for solutions of Navier-Stokes?

Given a solution $S$ of the Navier-Stokes equations, is there a way to make mathematically precise a statement like: "$S$ is turbulent in the spacetime region $U$"? And if such a definition exists, ...