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The Erwin Schroedinger Institute for Mathematical Physics

Eduard Feireisl (Academy of Sciences of the Czech Republic): Mathematics and Complete Fluid Systems

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.

At a glance

Type: SRF course
When: Mar 07, 2012 to
Jun 30, 2012
Where: Erwin Schrödinger Lecture Hall
Organizers: Joachim Schwermer (ESI, U Vienna)
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