Objectif The research of this proposal is focused on solving problems that involve the evolution of fluid interfaces. The project will investigate the dynamics of free boundaries arising between incompressible fluids of different nature. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or existence of solutions for all time. These contour dynamics issues are governed by fundamental fluid mechanics equations such as the Euler, Navier-Stokes, Darcy and quasi-geostrophic systems. They model important problems such as water waves, viscous waves, Muskat, interface Hele-Shaw and SQG sharp front evolution. All these contour dynamics frameworks will be studied with emphasis on singularity formation and global existence results, not only for their importance in mathematical physics, but also for their mathematical interest. This presents huge challenges which will in particular require the use of different tools and methods from several areas of mathematics. A new technique, introduced to the field by the Principal Investigator, has already enabled the analysis of several singularity formations for the water waves and Muskat problems, as well as to obtain global existence results for Muskat. The main goal of this proposal is to develop upon this work, going far beyond the state of the art in these contour dynamics problems for incompressible fluids. Champ scientifique natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencesclassical mechanicsfluid mechanicsfluid dynamicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationssocial scienceslaw Mots‑clés incompresible flow contour dynamics Euler Navier Stokes porous media SQG Muskat blow-up singularity Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-StG-2014 - ERC Starting Grant Appel à propositions ERC-2014-STG Voir d’autres projets de cet appel Régime de financement ERC-STG - Starting Grant Institution d’accueil UNIVERSIDAD DE SEVILLA Contribution nette de l'UE € 1 106 936,00 Adresse CALLE S. FERNANDO 4 41004 Sevilla Espagne Voir sur la carte Région Sur Andalucía Sevilla Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 106 936,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire UNIVERSIDAD DE SEVILLA Espagne Contribution nette de l'UE € 1 106 936,00 Adresse CALLE S. FERNANDO 4 41004 Sevilla Voir sur la carte Région Sur Andalucía Sevilla Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 106 936,00