Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution

CIRM, Luminy, Marseille

Date(s) : 23/09/2019 - 27/09/2019   iCal
0 h 00 min


Fluides inhomogènes: modèles asymptotiques et évolution d’interfaces
Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution

This conference is part of the ”Semaines CIRM-SMF” program and is dedicated to the mathematical analysis of non homogeneous models of fluid mechanics.
This project of conference follows the themes of the ANR-15-CE40-0011 INFAMIE. It has for vocation to bring together internationally recognized experts of every continents coming from various branches of mathematical fluid dynamics and young researchers being interested in the fluid mechanics and, more particularly, in the evolution of inhomogeneous fluids where problems of interfaces occur.

The PDEs modelling mixtures and the nonhomogeneous fluids arise naturally in numerous applications linked to the industry, the biology and the environment : distribution of pollutants, problems of sedimentation, etc. One of the major difficulties both from numerical and theoretical viewpoints is the evolution of a fluid presenting a jump of density along a curve of the plan or along a surface of the space (it can be seen as a toy model for a mixture of two fluids). This kind of problem can be tackled by two approaches almost orthogonal : technics of type ” free boundaries ” where we focus on the equation governing the evolution of the interface, or ”the global” approach consisting in solving the equation on all the domain, but in a functional setting containing discontinuous functions along an interface.

This conference will be the opportunity to make the state of the art on this subject which knew a considerable development since about fifteen years. Very diverse techniques were used going of simple estimates of energy to the analysis of Fourier (decomposition of Littlewood- Paley in particular) and to the theory of the analytical semi-groups and the maximal regularity. We hope that this conference will allow to present without taboo the tools of analysis coming into play in the study of the EDP (such as the equations of incompressible Navier-Stokes with variable density, or compressible Navier Stokes, the equations of Korteweg, Euler-Korteweg, etc.) modeling the nonhomogeneous fluids, and to propose new angles of attack.

Three mini-courses of 4 1/2 hours, and eighteen 40 minutes presentations by junior and senior researchers are scheduled. The conference will be more widely opened to another thirty participants that are interested in the theme, but do not wish to give a talk.

– A first mini-course given by Peer Christian Kunstmann (Karlsruhe university) will propose a panorama of the theory of the semi-groups and the properties of maximal regularity for the equations of parabolic type.
– The second mini-course, more forward-looking, will be dispensed by Pascal Auscher (CNRS, Université de Picardie Jules Verne) and will present very recent tools of harmonic analysis likely to give a new lighting to the study of the equations of Navier-Stokes type.
– Finally, the third mini-course, given by Sergey Gavrilyuk (Aix-Marseille Université) will concern the modelling of fluid-fluid diffuse interfaces.

Organizers :
Sylvie Monniaux (I2M, Marseille)
– Frédéric Charve (Université Paris-Est Créteil)
– Raphaël Danchin (Université Paris-Est Créteil)
– Boris Haspot (Université Paris-Dauphine)

Aix-Marseille Université (AMU)
Agence Nationale de la Recherche (ANR)
European Mathematical Society (EMS)
Institut de Mathématiques de Marseille (I2M)
LabEx Archimède
Laboratoire d’analyse et de mathématiques appliquées (LAMA)
Société Mathématique de France (SMF)
UPEC – Université Paris-Est Créteil
Ville de Marseille


Autre lien : CIRM


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