Ток векторного потенциала

Last modified by Alexey Popov on 2021/12/18 15:27

$\nabla \cdot \mathbf a = 4\pi G (\rho_u - \rho)$

$\nabla \cdot \boldsymbol \omega = 0$

$\nabla \times \mathbf a = -\frac{\partial\boldsymbol \omega}{\partial t}$

$\nabla \times \boldsymbol \omega = 4\pi\frac{G}{c^2}(\rho_u - \rho)\mathbf v +\frac{1}{c^2}\frac{\partial\mathbf a}{\partial t}$

$\oint \limits_{\mathbf {l}} \boldsymbol \omega\cdot d \mathbf {l} =4\pi\frac{G}{c^2}\rho_u \int \limits_{\mathbf {s}}\mathbf v \cdot d\mathbf s - 4\pi\frac{G}{c^2}\int \limits_{\mathbf {s}}\rho \mathbf v \cdot d\mathbf s + \frac{1}{c^2}\frac{d}{dt} \int \limits_{\mathbf {s}} \mathbf a \cdot d\mathbf s$

$\Delta \mathbf v = -4\pi\frac{G}{c^2}\rho \mathbf v$

$\mathbf v \sim \frac{1}{R}$

$\frac{\partial \mathbf v}{\partial t} = - \nabla \varphi - \mathbf a$

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Created by Alexey Popov on 2021/12/18 15:27

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