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Finite time singularities of smooth solutions for the 2D incompressible porous media (IPM) equation with a smooth source
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We establish the existence of smooth, finite-energy solutions to the 2D incompressible porous media equation (IPM), with a compactly supported uniformly smooth source, which develop singularities in finite time.
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Cited by 2 Pith papers
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Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1,\sqrt{\frac{4}{3}}-1-\epsilon}\cap L^2$ force
There exist compactly supported, smooth-before-blow-up solutions of the forced 2D Boussinesq equation that blow up in finite time with a uniformly C^{1,alpha} cap L^2 force for every alpha < sqrt(4/3)-1.
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Finite time blow-up in a 1D model of the incompressible porous media equation
For a new 1D boundary-layer model of the porous media equation with nonlocal velocity, smooth even data that vanish at the origin and increase toward the edge lose smoothness in finite time.
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