Mathematical Analysis of Models in Non-Newtonian Fluid Thermodynamics - NMOD042

• Title: Matematická analýza modelů termodynamiky nenewtonovských tekutin
• Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2018
• Semester: summer
• E-Credits: 3
• Hours per week, examination: summer s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: cancelled
• Language: Czech
• Teaching methods: full-time
• Guarantor: doc. RNDr. Miroslav Bulíček, Ph.D.; prof. RNDr. Josef Málek, CSc., DSc.
• Class: DS, matematické a počítačové modelování; DS, matematická analýza
• Classification: Mathematics > Mathematical Modeling in Physics
• Interchangeability : NMMO539
• Is incompatible with: NMMO539
• Is interchangeable with: NMMO539

Annotation

English

Dealing with mechanical and thermal processes described by non-Newtonian fluid thermodynamics in terms of system of partial differential equations represing the balance equations for mass, linear and angular momentum, energy and entropy for each bulk of material, we present several approaches and mathematical tools that are successfully incorporated in order to eastablish large data mathematical properties of both steady and unsteady flows of such classes of fluids. Particularly, the questions of existence, uniqueness, regularity and large time behavior of weak solutions are studied.

Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)

Czech

Cílem kursu budou vysvětlit různé metody a přístupy k existenční teorii pro systémy parciálních diferenciálních rovnic popisujících chování různých tříd nenewtonských tekutin.

Last update: T_MUUK (23.01.2007)

Aim of the course

English

The course aims to present methods that are used in investigating large data mathematical properties of flows of incompressible non-Newtonian fluids that are valid for large classes of constitutive relationships.

Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)

Czech

Cílem přednášky je přiblížit posluchačům metody, které se používají při studiu matematických vlastností proudění nestlačitelných nenewtonských tekutin, která platí pro libovolná data (geometrie, časový interval, počáteční podmínky, dané objemové zdroje) a pro co nejširší třídy konstitutivních vztahů.

Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)

Literature

J. Málek, K.R. Rajagopal: Mathematical issues concerning the Navier-Stokes equations and some of their generalizations. Handb. diff. equations. II, 371-459, 2005.

J. Málek, K. R. Rajagopal: Mathematical properties of the flows of incompressible fluids with pressure and shear rate dependent viscosities, Handb. Math. Fluid Dynamics IV, 2007.

P.L. Lions, N. Masmoudi: Global solutions for some Oldroyd models of non-Newtonian flows., Chinese Ann. Math. Ser. B 21 (2000), no. 2, 131--146.

Last update: T_MUUK (23.01.2007)

Teaching methods

English

Lecture course

Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)

Czech

přednáška

Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)

Syllabus

J. Málek, K.R. Rajagopal: Mathematical issues concerning the Navier-Stokes equations and some of their generalizations. Handb. diff. equations. II, 371-459, 2005.

J. Málek, K. R. Rajagopal: Mathematical properties of the flows of incompressible fluids with pressure and shear rate dependent viscosities, Handb. Math. Fluid Dynamics IV, 2007.

P.L. Lions, N. Masmoudi: Global solutions for some Oldroyd models of non-Newtonian flows., Chinese Ann. Math. Ser. B 21 (2000), no. 2, 131--146.

Last update: T_KMA (24.01.2007)