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Course, academic year 2019/2020
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Mathematical Methods in Mechanics of Non-Newtonian Fluids - NMMO539
Title in English: Matematické metody v mechanice nenewtonovských tekutin
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Guarantor: RNDr. Miroslav Bulíček, Ph.D.
prof. RNDr. Josef Málek, CSc., DSc.
Class: M Mgr. MOD
M Mgr. MOD > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Mathematical Modeling in Physics
Incompatibility : NMOD042
Interchangeability : NMOD042
Annotation -
Last update: T_MUUK (14.05.2013)
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.
Aim of the course -
Last update: prof. RNDr. Josef Málek, CSc., DSc. (13.10.2017)

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.

Course completion requirements -
Last update: prof. RNDr. Josef Málek, CSc., DSc. (13.10.2017)

The exam is based on the solution of selected homeworks and oral examination of methods and tools used in the anaysis of problems investigated and presented in the course.

Literature - Czech
Last update: prof. RNDr. Josef Málek, CSc., DSc. (13.10.2017)

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.

Research papers.

Teaching methods -
Last update: T_MUUK (14.05.2013)

Lecture course

Requirements to the exam -
Last update: prof. RNDr. Josef Málek, CSc., DSc. (13.10.2017)

The exam is based on the solution of selected homeworks and oral examination of methods and tools used in the anaysis of problems investigated and presented in the course.

Syllabus -
Last update: prof. RNDr. Josef Málek, CSc., DSc. (13.10.2017)

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.

and other suitable research papers.

 
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