. . "Matematick\u00E1 anal\u00FDza v termodynamice tekutin" . . "2008-12-16+01:00"^^ . . "Navier-Stokes-Fourier equations; fluid mechanics; qualitative properties of solutions"@en . "2005-01-01+01:00"^^ . . . . "2007-05-02+02:00"^^ . . "Mathematical analysis in thermodynamics of fluids"@en . "Navier-Stokes-Fourier equations" . "The aim of the present research proposal is to establish a coherent mathematical theory of viscous heat conducting fluids based on a suitable variational formulation of the problem consistent with the second law of thermodynamics. The main topics include: The existence of solutions on arbitrarily large time intervals with no restrictions on the size of data. The questions of uniqueness, boundedness, and stability of solutions with respect to the initial conditions and other parameters as the casemay be. The long-time behavior, convergence towards equilibria, and attractors. Sensitivity analysis with respect to the shape of the underlying spatial domain. The goal of the project are new theoretical results, the transfer of expertise by the training of students, and development of the existing international cooperation."@en . "26"^^ . . "26"^^ . . "Byla vybudov\u00E1na obecn\u00E1 existen\u010Dn\u00ED teorie pro syst\u00E9m Navierov\u00FDch Stokesov\u00FDch Fourierov\u00FDch rovnic zalo\u017Een\u00E1 na pojmu slab\u00E9ho \u0159e\u0161en\u00ED. Teorie p\u0159ipou\u0161t\u00ED libovoln\u011B velk\u00E1 data a je pou\u017Eiteln\u00E1 bez omezen\u00ED na d\u00E9lku \u010Dasov\u00E9ho intervalu. Pou\u017Eit\u00E9 konstitu\u010Dn\u00ED vztahy js"@cs . "Podstatou navrhovan\u00E9ho projektu je vybudov\u00E1n\u00ED ucelen\u00E9 matematick\u00E9 teorie vazk\u00FDch tepeln\u011B vodiv\u00FDch tekutin spo\u010D\u00EDvaj\u00EDc\u00ED v zaveden\u00ED varia\u010Dn\u00ED formulace \u00FAlohy zalo\u017Een\u00E9 na druh\u00E9m termodynamick\u00E9m z\u00E1konu. Hlavn\u00ED okruhy probl\u00E9m\u016F zahrnuj\u00ED: Vy\u0161et\u0159ov\u00E1n\u00ED existence \u0159e\u0161en\u00ED na libovoln\u011B dlouh\u00E9m \u010Dasov\u00E9m intervalu a bez omezen\u00ED na velikost dat. Zkoum\u00E1n\u00ED ot\u00E1zek jednozna\u010Dnosti, ohrani\u010Denosti a stability \u0159e\u0161en\u00ED vzhledem k po\u010D\u00E1te\u010Dn\u00EDm podm\u00EDnk\u00E1m a dal\u0161\u00EDm parametr\u016Fm \u00FAlohy. Chov\u00E1n\u00ED \u0159e\u0161en\u00ED pro velk\u00E9 \u010Dasy, konvergence k stacion\u00E1rn\u00EDm stav\u016Fm, atraktory. Stabilita \u0159e\u0161en\u00ED vzhledem ke tvaru prostorov\u00E9 oblasti. C\u00EDlem projektu je dosa\u017Een\u00ED nov\u00FDch teoretick\u00FDch v\u00FDsledk\u016F, vytvo\u0159en\u00ED tv\u016Fr\u010D\u00EDho prost\u0159ed\u00ED pro v\u00FDchovu mlad\u00FDch v\u011Bdc\u016F a prohlubov\u00E1n\u00ED mezin\u00E1rodn\u00ED spolupr\u00E1ce." . . "2007-12-31+01:00"^^ . . "A general existence theory has been developed for the Navier-Stokes-Fourier system based on the concept of weak solution. The theory admits arbitrarily large data and applies without any restriction on the length of the time interval. The constitutive re"@en . . "0"^^ . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/05/0164"^^ . . . "GA201/05/0164" . " fluid mechanics" . "1"^^ . . . "1"^^ . .