Tagged Questions

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.

11k views

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 ...
255 views

61 views

88 views

Implementation of a simulation of an incompressible Newtonian fluid with uniform density

Let $d\in\left\{2,3\right\}$ and $\Omega\subseteq\mathbb R^d$ be a bounded domain. I want to simulate an incompressible Newtonian fluid with uniform density $\rho$ and viscosity $\nu$. The evolution ...
118 views

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 $i$-...
101 views

If $F∈H^{-1}(Ω,ℝ^d)$ and $∃p∈\mathcal D'(Ω):\left.F\right|_{\mathcal D(Ω,ℝ^d)}=∇p$, then $∃\overline p∈H^{-1}(Ω):F=∇\overline p$

Let $d\in\mathbb N$ $\Omega\subseteq\mathbb R^d$ be open $\mathcal D(\Omega):=C_c^\infty(\Omega)$ and $\mathcal D(\Omega,\mathbb R^d):=C_c^\infty(\Omega,\mathbb R^d)$ $H^{-1}(\Omega):=H_0^1(\Omega)'$...
300 views

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 ...
798 views

66 views

Finding stagnation points and stream function

Sorry for the lack of latex. The question I want to ask would need all this info and it would take very long to write it. (a) Irrotational flow means $\nabla \times \textbf u =0$ so we can define ...
74 views

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 = -\frac{\delta\psi}{\...
$\overrightarrow f = 3x\overrightarrow i - 3y\overrightarrow j$ $\overrightarrow g = 3x\overrightarrow i + 3y\overrightarrow j$ If I calculate the divergence of $f$ I get $0$. If I calculate the ...