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Oscillatory solutions to problems in fluid mechanics

Attention

There are new slides available!


It is going to take place from 10am until 12am and another slot from 2pm to 4pm.

Schedule

Schedule
Daily
10:00 - 12:00
14:00 - 16:00
Lecture
MA415
Prof. RNDr. Eduard Feireisl, DrSc.

Prof. RNDr. Eduard Feireisl, DrSc.
Secretary
MA568

Description

Lupe

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss mechanisms preventing oscillations/concentrations and make a short excursion into the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results:

   1. Many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution)
  2. The solutions are not determined uniquely by their initial data. We examine the basic analytical tool  behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics.

Content

  • Motivation
  • Discussion of mechanisms preventing oscilliations/concentrations
  • Excursion into the theory of compensated compactness and the Div-Curl-Lemma
  • Strong and weak solutions of the compressible Euler system
  • Oscillatory solutions to the compressible Euler system
  • Ill-posedness of the Euler-system
  • Method of convex integration applied to problems in fluid mechanics

Requirements

Basic theory of functional analysis e.g. weak convergence, Baire category theorem etc., Sobolev Spaces, variatinal furmulation for linear and nonlinear problems

Material for the lecture

Zusatzinformationen / Extras

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