Smooth initial data for 1D compressible Euler with vacuum boundary can develop gradient blowup at the boundary in finite time.
,Falqui, G., Ortenzi, G.,Pedroni, M., Pitton, G., On the “Vacuum” Dam-Break Problem: Exact Solutions and Their Long Time Asymptotics,SIAM J
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Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations
Smooth initial data for 1D compressible Euler with vacuum boundary can develop gradient blowup at the boundary in finite time.