Objectif The main goal of the present research proposal is to build up a general mathematical theory describing the motion of a compressible, viscous, and heat conductive fluid. Our approach is based on the concept of generalized (weak) solutions satisfying the basic physical principles of balance of mass, momentum, and energy. The energy balance is expressed in terms of a variant of entropy inequality supplemented with an integral identity for the total energy balance.We propose to identify a class of suitable weak solutions, where admissibility is based on a direct application of the principle of maximal entropy production compatible with Second law of thermodynamics. Stability of the solution family will be investigated by the method of relative entropies constructed on the basis of certain thermodynamics potentials as ballistic free energy.The new solution framework will be applied to multiscale problems, where several characteristic scales become small or extremely large. We focus on mutual interaction of scales during this process and identify the asymptotic behavior of the quantities that are filtered out in the singular limits. We also propose to study the influence of the geometry of the underlying physical space that may change in the course of the limit process. In particular, problems arising in homogenization and optimal shape design in combination with various singular limits are taken into account.The abstract approximate scheme used in the existence theory will be adapted in order to develop adequate numerical methods. We study stability and convergence of these methods using the tools developed in the abstract part, in particular, the relative entropies. Champ scientifique natural sciencesphysical sciencesthermodynamicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicsapplied mathematicsnumerical analysissocial scienceslaw Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Appel à propositions ERC-2012-ADG_20120216 Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil MATEMATICKY USTAV AV CR V.V.I. Contribution de l’UE € 726 320,00 Adresse ZITNA 609/25 115 67 Praha Tchéquie Voir sur la carte Région Česko Praha Hlavní město Praha Type d’activité Other Chercheur principal Eduard Feireisl (Prof.) Contact administratif Jiří Rákosník (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire MATEMATICKY USTAV AV CR V.V.I. Tchéquie Contribution de l’UE € 726 320,00 Adresse ZITNA 609/25 115 67 Praha Voir sur la carte Région Česko Praha Hlavní město Praha Type d’activité Other Chercheur principal Eduard Feireisl (Prof.) Contact administratif Jiří Rákosník (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée