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SUMMARY:On a macroscopic description of the Saffman-Taylor instability.
DTSTART:20250520T131500Z
DTEND:20250520T141500Z
DTSTAMP:20260611T031500Z
UID:indico-event-14354@indico.math.cnrs.fr
DESCRIPTION:Speakers: Björn Gebhard (Universität Münster)\n\nWe conside
 r the incompressible porous media equation (IPM) describing the evolution 
 of an incompressible fluid in a porous medium subject to gravity. The init
 ial data of our interest consists of a (not necessarily flat) interface se
 parating a heavier fluid with homogeneous density $\\rho_+>0$ from a light
 er fluid with homogeneous density $\\rho_-\\in(0\,\\rho_+)$\, with the hea
 vier one being above the lighter one. Due to the gravity term this situati
 on is in real world scenarios unstable and mathematically ill-posed as an 
 initial value problem.The talk addresses the question of recovering well-p
 osedness on the level of averaged solutions (convex integration subsolutio
 ns) by means of a selection based on maximal potential energy dissipation.
  We will see that this criterion leads to a nonlocal hyperbolic conservati
 on law - the "macroscopic IPM" system - which is consistent with the relax
 ation of Otto based on the gradient flow structure of IPM. In the second p
 art of the talk we will discuss the construction of an entropy solution fo
 r macroscopic IPM emanating from a real analytic initial interface. \nThi
 s is based on a joint work with \\'Angel Castro and Daniel Faraco.\n \n\n
 https://indico.math.cnrs.fr/event/14354/
LOCATION:Amphi Jordan (ICJ)
URL:https://indico.math.cnrs.fr/event/14354/
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