instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Mixing solutions for the Muskat problem.
Fecha: Del 27.04.2017 al 28.04.2017 De 12.30 a 14.00
Lugar: Seminario I (IMUS), Edificio Celestino Mutis
The IPM equations model the motion of an incompressible fluid with  variable density  in a porous media and under the force of gravity.  The Muskat problem deals with a situation in which the density of the  fluid take two different and constant values. This problem is  ill-posed in Sobolev's spaces for an unstable situation in which the  part of the fluid with larger density is above. In this course we will  present a construction of weak solution of the IPM equation which  cosist of the mixing of the two densities for the Muskat problem.  First of all we will introduce the technique of the convex integration  applied to the IPM equations and after that we will go through the  main steps to construct the mixing solutions.