= Linearized Euler equations
The linearized Euler equations retain only first-order perturbations about a specified inviscid fluid state. Together with the linearized <continuity equation> and a pressure-density constitutive relation, they describe small-amplitude <acoustic waves>. About a uniform resting state, $\rho_0\partial_t\mathbf u'=-\nabla p'$, $\partial_t\rho'+\rho_0\nabla\cdot\mathbf u'=0$, and an isentropic pressure perturbation has $p'=c_0^2\rho'$. Gradients and advection of a moving background must be retained when its variation is not negligible.
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