Fluid dynamics is a branch of physics that studies the motion of liquids or 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 ...
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reference for Navier-Stokes equation

For understanding the Navier-Stokes equations, are there any references which may include one or more of the followings: mathematical rigorousness motivation preliminaries introduction etc.
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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 ...
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Complex parametrization of Airplane wing?

I read once about complex parametrization with fluid-dynamics objects such as airplane wings, something related Rieman Zeta function. What are the mathematical models this kind of things such as ...
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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 ...
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Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
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Is Euler's lemma of fluid mechanics a nonlinear version of Liouville's theorem of ODEs?

Liouville's Theorem Consider the following linear system of ordinary differential equations: $$\tag{1} \dot{\mathbf{x}}=A(t)\mathbf{x}(t).$$ Let $\mathbf{x}_1, \mathbf{x}_2, \ldots, ...
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Streamlines - Pathlines

Construct and draw the streamlines of the velocity field $u=az-bt, v=\frac{b}{4}z-cy, w=2(a-1)$. Calculate $c$ (as a function of the constants $a$, $b$) such that the flow field ...
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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 ...
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Continuity equation on manifolds

Mass conservation is usually written as $$\frac{\partial \rho}{\partial t} + \operatorname{div}(\rho \boldsymbol v) = 0$$ $\rho$ is the density and $\boldsymbol v$ is the fluid velocity. My attempt ...
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Stress vector - Stress tensor

Is the definition of the stress vector the following? The stress vector is the force per unit surface. The stress tensor is the matrix $\{\sigma_{ij}(x,t)\}$ and its $(i,j)$-component is the ...
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How to differentiate Complex Fluid Potential

I have $$F(z) = \phi + i\psi$$ Also, it is given that $$u = \frac{\delta \phi}{\delta x}, \ \ v = \frac{\delta\phi}{\delta y}$$ and $$u = \frac{\delta \psi}{\delta x}, \ \ v = ...
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Plotting Streamlines Maple

I wonder if anybody could help with this. I've been asked to plot the streamlines of the complex potential $\Omega(z)=Uz + \frac{m}{2\pi}ln(z)$ to which I get the stream function ...
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fluid dynamics in polar coordinates

On page 12 of Malham's fluid dynamics notes the following flow field is considered: $\boldsymbol u= (u,v) = (kx, -ky)$. It's easy to see in these Cartesian coordinates that this is solenoidal: ...
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Solving a system of two second order ODEs using Runge-Kutta method (ode45) in MATLAB

I'm trying to solve the system of differential equations outlined in Von Karman's rotating disk flow. I got them into a system of ordinary differential equations: F(n), G(n), H(n) $$F'' = -G^2 + F^2 ...
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Fluid Forces using Calculus (Find Work Done)

A tank in the shape of an inverted right circular cone has height 12 meters and radius 11 meters. It is filled with 6 meters of hot chocolate. Find the work required to empty the tank by pumping the ...
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How to integrate twice of this viscous term?

I am reading a paper, and I do not understand why the author said the following term when integrated twice will become, $\int\limits_\Omega {{\rm{d}}\Omega {{\bf{\psi }}^{\bf{u}}}\cdot\nabla ...