Note on the dissipation for the general Muskat problem
Susanna V. Haziot, Beno\^it Pausader
TL;DR
This paper provides an elementary proof of a key inequality related to the dissipation in the Muskat problem, extending its applicability beyond previous limitations.
Contribution
It offers a new, simplified proof of a fundamental inequality in the Muskat problem, applicable in more general settings.
Findings
Proved a generalized inequality for the Muskat problem.
Extended the applicability of the dissipation inequality.
Simplified the proof of a key mathematical property.
Abstract
We consider the dissipation of the Muskat problem and we give an elementary proof of a surprising inequality of Constantin-Cordoba-Gancedo-Strain which holds in greater generality.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Navier-Stokes equation solutions · Contact Mechanics and Variational Inequalities