The second iterate of the Muskat equation in supercritical spaces

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Free boundary problems for PDEs (35R35) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Cites Work

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On the second iterate for critically diffusive active scalar equations
Porous media: The Muskat problem in three dimensions
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
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Well-posedness of the Muskat problem with $H^2$ initial data
A note on interface dynamics for convection in porous media
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The second iterate for the Navier-Stokes equation
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A paradifferential approach for well-posedness of the Muskat problem
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Endpoint Sobolev theory for the Muskat equation
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The Muskat problem with 𝐶¹ data
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Existence time for the Camassa-Holm equation and the critical Sobolev index
Global well‐posedness for the one‐phase Muskat problem
Global Regularity for Gravity Unstable Muskat Bubbles

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