Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [fluid-dynamics]

For questions about fluid dynamics which studies the flows of fluids and involves analysis and solution of partial differential equations like Euler equations, Navier-Stokes equations, etc. Tag with [tag:mathematical-physics] if necessary.

Fluid dynamics is a branch of physics that studies the the flows of fluids-liquids and gases, which involves analysis and solution of partial differential equations like Euler equations, Navier-Stokes equations, etc.

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Is the problem that Prof Otelbaev proved exactly the one stated by Clay Mathematics Institute?

Recently, mathematician Mukhtarbay Otelbaev published a paper Existence of a strong solution of the Navier-Stokes equations, in which he claim that he solved one of the Millennium Problems: existence and smoothness of the Navier-Stokes Equation.…
Fang Hung-chien
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How to go about studying chaos theory/dynamical systems/fluid dynamics in grad school with a physics background?

I'm turning to you as I find myself in need of help as to how to best go about studying something related to chaos theory/dynamical systems/fluid dynamics in postgraduate school. I'm currently in my third year of physics and my first question would…
Ryker
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Good introductory book on fluid dynamics

I am interested in getting a good introductory book to fluid dynamics. I am a first year PhD student in Mathematics. My project involves a simplification of the Navier-Stokes equations. But I don't have any background whatsoever on fluid dynamics…
chango
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Did I just solve the Navier-Stokes Millennium Problem?

I think I may have just solved a Millennium Problem. I found an exact 3D solution to Navier-Stokes equations that has a finite time singularity. The velocity, pressure, and force are all spatially periodic. The solution has a time singularity at…
A.G.
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Existence and uniqueness of Stokes flow

What are the solution existence and uniqueness conditions for Stokes' flow? $$\begin{gathered} \nabla p = \mu \Delta \vec{u} + \vec{f} \\ \nabla \cdot \vec{u} = 0 \end{gathered}$$ Maybe you could also provide some articles or books about the topic?…
Džuris
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Coffee and regular polygons

To save some money, I decided to brew my own morning-fix coffee and skip buying it from the coffee shop. BTW, I drive to work and put my coffee cup in between the two front seats. While driving on the freeway (especially while driving through the…
Lord Soth
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Why can't you simulate isotropic fluid flow on a square lattice?

There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you move the molecules from cell to adjacent cell at…
MJD
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Vorticity equation in index notation (curl of Navier-Stokes equation)

I am trying to derive the vorticity equation and I got stuck when trying to prove the following relation using index notation: $$ {\rm curl}((\textbf{u}\cdot\nabla)\mathbf{u}) = (\mathbf{u}\cdot\nabla)\pmb\omega - ( \pmb\omega…
Casio
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Connection between distributional and renormalized solutions for Boltzmann equation

I have a problem understanding the meaning of a distributional solution. Let me tell you the context the problem appeared: I read through some papers by DiPerna and Lions concerning the Cauchy Problem for Boltzmann Equations ("R.J. DiPerna and P.L.…
Montaigne
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Translation of John Nash's 1962 Navier-Stokes paper

Is anyone aware of an English translation of the following paper of John Nash? John Nash, Le Probleme de Cauchy pour les equations differentielles d'un fluide general, Bulletin de la Société Mathématique de France, tome 90 (1962), p. 487-497.
dobo
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Fluid mechanics resources for pure mathematicians?

I'm currently taking a course on fluid mechanics, and I'm finding it very difficult to become motivated and interested. I've always been more interested in the pure math side of my courses, and love finding the links between pure and applied…
hasnohat
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Helicity is Conserved

In fluid mechanics, the helicity is defined as $$\int_{R^3} u(x,t)\cdot \omega(x,t),$$ where $u(x,t)$ is a smooth solution of the Euler equations $$\partial_tu + (u \cdot \nabla) u = -\nabla p$$ $$\nabla \cdot u = 0,$$ and $\omega$ is the…
MarsOneRover
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Reynolds transport theorem: link with the Lie derivative?

In this Wikipedia article (see "Higher dimensions") there seems to be a connection between the Reynolds transport theorem (here) and the Lie derivative: $$\frac{d}{dt}\int_{\Omega(t)}\omega=\int_{\Omega(t)} i_{\vec{\textbf…
Quillo
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Solving a simple Shallow Water model

I need to solve with basic methods this simple Shallow Water Model: $$\begin{bmatrix}h\\ hv\end{bmatrix}_t+\begin{bmatrix}hv\\ hv^2+\frac{1}{2}gh^2\end{bmatrix}_x=\begin{bmatrix}0\\ 0\end{bmatrix}$$ where $h$ is the height of the water, $v$ is the…
Quiet_waters
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Stirring a square cup results in a strange pattern. What's the math behind it?

I came across this picture earlier today: https://i.sstatic.net/lMrkU.jpg and it left me kind of baffled. Can anyone explain the mathematics behind the reason why this is happening?
Michael Smith
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