Wednesday August 21 at 3:00 PM to 4:00 PM in SAS 4201
Differential Equations
Angot Philippe, AixMarseille Université, Mathematical modeling and analysis towards the open problem of flow at a fluidporous interface
We discuss mathematical modeling and analysis of the incompressible viscous flow at the interface of permeable media. Very recently, a simplified theory with asymptotic modeling and related approximations was extensively developed by [Angot et al., 2017] to provide physically relevant jump interface conditions for the two or threedimensional noninertial flow at the interface of a permeable medium. The results of wellposedness analysis for three problems issued from this asymptotic model and covering the whole porosity range will be described. Finally, some perspectives are proposed to deal with the multidimensional inertial flow by the same asymptotic modeling which supplies nonlinear jump interface conditions. We shall explain why this nonlinear model is likely to yield the global solvability in time.
