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ESI Senior Research Fellow Programme, spring term 2012
Mathematics and complete fluid systems
Course of advanced graduate lectures by
Professor Eduard Feireisl
(Insitute of Mathematics, Academy of Sciences of the Czech Republic)
Start: Wednesday, March 7, 2012
Lecture course with integrated Seminar
(VU 250132): Wednesday 9-12
ESI, Erwin Schrödinger Lecture Hall
Abstract:
This Lecture Course is devoted to the modern mathematical theory of
complete fluid systems - the fluid flows satisfying the basic physical
principles of conservation of mass, momentum, and energy. Our approach
is based on the concept of weak solution introduced in the monograph [M].
The main topics include:
- Basic equations of mathematical fluid dynamics, the Navier-Stokes-Fourier system
- Weak vs. strong formulation, basic properties, advantages, shortcomings
- Nonlinear equations and a priori bounds, global dissipation inequality and related questions
- Relative entropies, weak-strong uniqueness, long-time behavior of complete fluid systems
- The property of (weak) sequential stability
- Principal ideas of the mathematical theory of global-in-time large data solutions, the effective viscous pressure, commutator estimates, div-curl lemma
- More advanced topics related to complete fluid systems, model reduction and singular limits
BIBLIOGRAPHY
[M] E. Feireisl and A. Novotny: Singular limits in thermodynamics of viscous fluids. Birkhäuser-Verlag, Basel, 2009.
ESI Senior Research Fellow Programme coordinated by Prof. Piotr
T. Chrusciel, Gravitational Physics , Faculty of Physics, University
of Vienna, Währinger Straße 17, A-1090 Wien
(piotr.chrusciel@univie.ac.at)
and Prof. Adrian Constantin, Institute of Mathematics, University of
Vienna, Nordbergstraße 15 (UZA +IV), A-1090 Wien,
(adrian.constantin@univie.ac.at).
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