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Results tagged with fluid-dynamics
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user 21907
3
votes
Solving Stokes Equations using 3D Fourier transforms
Let me change your notations slightly: you work in three dimensions and you want to compute
$$
u_{jk}(x)=\int e^{2i\pi x\cdot \xi} \frac{\xi_j\xi_k}{\vert \xi\vert^4} d\xi,
$$
where the integral shoul …
- 16.2k
4
votes
Accepted
Vorticity equation for incompressible 2D fluid dynamics
The vorticity equation for the Euler equation in 3D is, with $\omega=\text{curl } v$,
$$
\dot\omega + (v\cdot\nabla)\omega-(\omega\cdot\nabla)v=0,
$$
so that if $v$ is two-dimensional, i.e.
$
v=\begin …
- 16.2k
1
vote
problem related to Airy functions
I recommend to look at pages 213-4-5 in the first volume of Hörmander's ALPDO, Springer Grundlehren, 256. In my opinion this is the shortest and most elementary introduction to Airy functions.
- 16.2k