S5B3 - Graduate Seminar on New Developments in Partial Differential Equations (winter term 2013/14)
Questions of Statistical Hydromechanics
Instructors: Prof. Dr. Herbert Koch, Prof. Dr. Stefan Müller
For questions please contact Christian Zillinger (zill at math.uni-bonn.de)
The long time behaviour of two dimensional incompressible and inviscid fluids will be studied in the seminar. Fluids modelled by the two dimensional Euler equation in metereology and other fields often show a strikingly simple and intuitive dynamics of vortices. This poses a challenge for the mathematical understanding of the two dimensional Euler equations. While a rigorous understanding is out of reach there are many heuristic and successful ideas from physics.
In the seminar we will study rigorous formulations and results, often under simplifying assumptions.
Literature
Author | Title | Source/Publisher |
---|---|---|
Sverak | Topics in Mathematical Physics (lectures 29-40) | http://www.math.umn.edu/~sverak/course-notes2011.pdf |
Batchelor | An Introduction to Fluid Dynamics | Cambridge Univ. Press, 2010 |
Yudovich | Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid | http://ams.mpim-bonn.mpg.de/mathscinet-getitem?mr=1312975 |
Turkington | Statistical equilibrium measures and coherent states in two-dimensional turbulence | Communications in Pure and Applied Mathematics, Vol. LII, No. 7, 1999, pp. 781-811 |
Majda, Wang | Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows | Springer, 2007 |
Arnold, Khesin | Topological methods in hydrodynamics | Springer, 2009 |
Khesin, Wendt | The geometry of infinite dimensional groups | Springer, 1999 |
Drazin | Hydrodynamic stability | Cambridge University Press, 1982 |
Villani | Landau damping | main work and survey, lecture notes |
Madmoudi, Bedrossian | Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations | arXiv |
Lin, Zeng | Inviscid dynamical structures near Couette flow | arxiv |
Li,Lin | A resolution of the Sommerfeld Paradox | arxiv |
Dates:
The seminar consists of three blockseminars on: 8.11.13 , 13.12.13,17.01.14
The first seminar will take place in room 2.025 starting at 9:00 (not 9:15).
- 08.11.13
Times Speaker Title Reference 09:00-10:00 Lukas Pieronek The Euler equation: formulations and properties Majda&Bertozzi (chapters 1,2.1) 10:15-11:15 Marcel Graus Beal-Kato-Majda: Well-posedness and blow-up Majda&Bertozzi, (chapters 2.5,3.3) 11:45-12:45 Lukas Matuschek Well-posedeness for L∞ solutions Majda&Bertozzi(chapter 8.2); Yudovich 13:30-14:30 Jan Krautter Classical stability results(Rayleigh, Fjortoft, Arnold) Drazin(section 22); Arnold&Khesin; Khesin&Wendt - 13.12.13
Times Speaker Title Reference 10:15-11:15 Thilo Simon Constraints and weak∗ convergence Sverak:29.2,32,33.1 11:45-12:45 Susanne Gammer Statistical Mechanics and Entropy Sverak:31,36 13:30-14:30 Richard Höfer Entropy, Turkington Sverak;Turkington 14:45-15:45 Thomas Vogt Orbits and Variation Sverak:35,38 ;Turkington - 17.01.14
Times Speaker Title Reference 09:00-10:00 Ksenia Fedosova A variational formulation of Euler's equation Arnold&Khesin 10:30-11:30 Matthäus Pawelczyk Scattering for NLS 11:45-12:45 Marcel Dengler Free transport and linear Landau damping Villani's script: chapter 3 13:30-14:30 Florian Schweiger Linear damping for Couette flow and behaviour of the nonlinear equation Lin&Zeng 14:45-15:45 Shaoming Guo The Sommerfeld paradox Li&Lin