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Finite-time blowup for 2D unforced IPM

Dai, Mimi
arXiv (All) · Papers
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35q35analysis-of-pdes
We construct an odd smooth initial density for the unforced incompressible porous media (IPM) equation on $\mathbb T^2$ whose solution develops a finite-time blowup. The components $\partial_{x_2}ρ(t,0)$ and $\partial_{x_1}u_1(t,0)$ tend to $+\infty$ as the maximal smooth existence time is approache
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