= Solution
The <material derivative> $\boxed{D/Dt=\partial_t+\mathbf u\cdot\nabla}$ measures change while following a moving gas parcel. The four equations respectively express \b[<mass conservation>], \b[<momentum conservation>], \b[internal-energy balance], and the \b[<ideal gas law>]. The first accounts for <density> change under expansion or compression. The second is Newton's law with <pressure> as the only force. In the third the specific internal energy is $c_vT$ and <pressure> work $-p\nabla\cdot\mathbf u$ heats compression and cools expansion. The fourth relates thermodynamic <pressure>, <density> and temperature; $R$ is the gas constant per unit mass.
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