Year: 2026
Type: preprint
Abstract: We construct mixing solutions to the incompressible porous media equation for fully unstable Muskat initial data. The mixing zone expands linearly in time around an evolving central interface. Our approach combines the $h$-principle with the inversion of the associated Birkhoff-Rott operator, required when the viscosities differ. A key ingredient is to formulate this inversion in terms of the Saffman-Taylor function rather than the vorticity. This considerably simplifies the analysis and may be of independent interest for the Muskat problem.
Source: arXiv (Cornell University)
Authors: Luna-Velasco, Paula, Mengual, Francisco
Institutions: Universidad de Granada, Universidad de Sevilla
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223842549