Objetivo Important problems in science often involve structures on several distinct length scales. Two typical examples are fine phase mixtures in solid-solid phase transitions and the complex mixing patterns in turbulent or multiphase flows. The microstructures in such situations influence in a crucial way the macroscopic behavior of the system, and understanding the formation, interaction and overall effect of these structures is a great scientific challenge. Although there is a large variety of models and descriptions for such phenomena, a recurring issue in the mathematical analysis is that one has to deal with very complex and highly non-smooth structures in solutions of the associated partial differential equations. A common ground is provided by the analysis of differential inclusions, a theory whose development was strongly influenced by the influx of ideas from the work of Gromov on partial differential relations, building on celebrated constructions of Nash for isometric immersions, and the work of Tartar in the study of oscillation phenomena in nonlinear partial differential equations. A recent success of this approach is provided by my work on the h-principle in fluid mechanics and Onsager's conjecture. Against this background my aim in this project is to go significantly beyond the state of the art, both in terms of the methods and in terms of applications of differential inclusions. One part of the project is to continue my work on fluid mechanics with the ultimate goal to address important challenges in the field: providing an analytic foundation for the K41 statistical theory of turbulence and for the behavior of turbulent flows near instabilities and boundaries. A further aim is to explore rigidity phenomena and to attack several outstanding open problems in the context of differential inclusions, most prominently Morrey's conjecture on quasiconvexity and rank-one convexity. Ámbito científico natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Palabras clave Fluid mechanics Turbulence Compensated Compactness h-principle Differential Inclusions Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-2016-COG - ERC Consolidator Grant Convocatoria de propuestas ERC-2016-COG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-COG - Consolidator Grant Institución de acogida UNIVERSITAET LEIPZIG Aportación neta de la UEn € 1 860 875,00 Dirección RITTERSTRASSE 26 04109 Leipzig Alemania Ver en el mapa Región Sachsen Leipzig Leipzig 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 € 1 860 875,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo UNIVERSITAET LEIPZIG Alemania Aportación neta de la UEn € 1 860 875,00 Dirección RITTERSTRASSE 26 04109 Leipzig Ver en el mapa Región Sachsen Leipzig Leipzig 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 € 1 860 875,00
