In the book about fluid-mechanics Landau in the first pages in the isentropic case from(adsbygoogle = window.adsbygoogle || []).push({});

[tex] dw=\frac{dp}{\rho}[/tex]

deduces

[tex] \nabla w=\frac{\nabla p}{\rho}[/tex]

but I can't understand... in its derivation dw and dp are material differential ([tex]dw=w(x+vdt,t+dt)-w(x,t)[/tex]) in my view) so writing it explicitely I was only able to deduce:

[tex](\nabla w-\frac{\nabla p}{\rho})\vec{v}=\partial_t(w-\frac{p}{\rho})[/tex]

but nothing more...

what am I missing?

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# Landau fluid mechanics- mathematical passage

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