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I'm trying to understand the derivation of (linearized) pertubation equations given in my lecture.

As usual the density and velocity fields are split into a homogeneous and an inhomogeneous part:

[tex]\rho(t,x) = \rho_0(t) + \delta \rho(x,t)[/tex]

[tex]\vec{v}(t,x) = \vec{v_0}(t) + \vec{\delta v}(x,t)[/tex]

Then (and that is what I don't understand) the claim is made that the background quantrities need to separately fullfill mass conservation. In other words:

[tex]\frac{\partial \rho_0}{\partial t} + \rho_0 \nabla * \vec{v_0} = 0[/tex]

Any idea where this comes from?

Many thanks in advance!

Angelos

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# Derivation of (linearized) perturbation equations

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