I am studying Lie derivatives and there is this question I cannot solve. The text says that is one transport equation. Anyone knows the reason for this name?
Yet, I am searching for any identity that leaves me to conclude that $\frac{d}{dt}\int_{\phi_t(U)}\omega_t = \int_{\phi_t(U)}(\partial_t\omega_t + L_X\omega_t)$?
Where $L_x\omega_t$ is the Lie derivative of $\omega_t$, a $p-$form that changes smoothly with $t$ and $\phi_t$ is the flow of $X$.
I appreciate any help.