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• W3098629791 abstract "We show the existence of infinitely many admissible weak solutions for the incompressible porous media equations for all Muskat-type initial data with $${C^{3,alpha}}$$ -regularity of the interface in the unstable regime and for all non-horizontal data with $${C^{3,alpha}}$$ -regularity in the stable regime. Our approach involves constructing admissible subsolutions with piecewise constant densities. This allows us to give a rather short proof where it suffices to calculate the velocity and acceleration at time zero - thus emphasizing the instantaneous nature of non-uniqueness due to discontinuities in the initial data." @default.
• W3098629791 created "2020-11-23" @default.
• W3098629791 creator A5077855474 @default.
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• W3098629791 date "2018-08-29" @default.
• W3098629791 modified "2023-10-18" @default.
• W3098629791 title "Piecewise Constant Subsolutions for the Muskat Problem" @default.
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• W3098629791 doi "https://doi.org/10.1007/s00220-018-3245-2" @default.
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