Every sufficiently small smooth compact perturbation of a constant state in 3D irrotational compressible Euler blows up in finite time, with the expected lifespan.
and Moncrief, V.Elliptic-Hyperbolic Systems and the Einstein Equations.Ann
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Inevitable shock formation for 3-D compressible Euler flows
Every sufficiently small smooth compact perturbation of a constant state in 3D irrotational compressible Euler blows up in finite time, with the expected lifespan.