Obiettivo 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. Campo scientifico natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencesclassical mechanicsfluid mechanicsfluid dynamicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationssocial scienceslaw Parole chiave incompresible flow contour dynamics Euler Navier Stokes porous media SQG Muskat blow-up singularity Programma(i) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Argomento(i) ERC-StG-2014 - ERC Starting Grant Invito a presentare proposte ERC-2014-STG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-STG - Starting Grant Istituzione ospitante UNIVERSIDAD DE SEVILLA Contribution nette de l'UE € 1 106 936,00 Indirizzo CALLE S. FERNANDO 4 41004 Sevilla Spagna Mostra sulla mappa Regione Sur Andalucía Sevilla Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 106 936,00 Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo netto dell'UE Espandi tutto Riduci tutto UNIVERSIDAD DE SEVILLA Spagna Contribution nette de l'UE € 1 106 936,00 Indirizzo CALLE S. FERNANDO 4 41004 Sevilla Mostra sulla mappa Regione Sur Andalucía Sevilla Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 106 936,00
