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Mixing zone dynamics for the Saffman-Taylor instability with viscosity jump
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.
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BibTeX
@misc{lunavelasco2026mixing,
title = {{Mixing zone dynamics for the Saffman-Taylor instability with viscosity jump}},
author = {Paula Luna-Velasco and Francisco Mengual},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34504},
eprint = {2610.34504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34504},
}
RIS
TY - UNPB
TI - Mixing zone dynamics for the Saffman-Taylor instability with viscosity jump
AU - Paula Luna-Velasco
AU - Francisco Mengual
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34504
UR - https://arxiv.org/abs/2610.34504
AB - 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.
ER -