Smooth initial data for 1D compressible Euler with vacuum boundary can develop gradient blowup at the boundary in finite time.
C., Global existence and asymptotic behavior of affine motion of 3D ideal fluids surrounded by vacuum,Arch
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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.