Mathematical Thermodynamics of Fluids


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 Nazionalità Coordinatore Czech Republic [CZ]
 Totale costo 726˙320 €
 EC contributo 726˙320 €
 Programma 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)
 Code Call ERC-2012-ADG_20120216
 Funding Scheme ERC-AG
 Anno di inizio 2013
 Periodo (anno-mese-giorno) 2013-05-01   -   2018-04-30


# participant  country  role  EC contrib. [€] 

 Organization address address: ZITNA 609/25
city: PRAHA 1
postcode: 115 67

contact info
Titolo: Dr.
Nome: Ji?í
Cognome: Rákosník
Email: send email
Telefono: +420 222 090 762
Fax: +420 222 090 701

CZ (PRAHA 1) hostInstitution 726˙320.00

 Organization address address: ZITNA 609/25
city: PRAHA 1
postcode: 115 67

contact info
Titolo: Prof.
Nome: Eduard
Cognome: Feireisl
Email: send email
Telefono: +420 222090737
Fax: +420 222090701

CZ (PRAHA 1) hostInstitution 726˙320.00


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

entropies    singular    entropy    stability    solutions    scales    relative    solution    theory    energy    limits    thermodynamics    balance    physical    weak    abstract   

 Obiettivo del progetto (Objective)

'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.'

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