Objetivo 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. Ámbito científico natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencesclassical mechanicsfluid mechanicsfluid dynamicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationssocial scienceslaw Palabras clave incompresible flow contour dynamics Euler Navier Stokes porous media SQG Muskat blow-up singularity Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-StG-2014 - ERC Starting Grant Convocatoria de propuestas ERC-2014-STG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-STG - Starting Grant Institución de acogida UNIVERSIDAD DE SEVILLA Aportación neta de la UEn € 1 106 936,00 Dirección CALLE S. FERNANDO 4 41004 Sevilla España Ver en el mapa Región Sur Andalucía Sevilla Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 106 936,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo UNIVERSIDAD DE SEVILLA España Aportación neta de la UEn € 1 106 936,00 Dirección CALLE S. FERNANDO 4 41004 Sevilla Ver en el mapa Región Sur Andalucía Sevilla Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 106 936,00