S5B3 - Graduate Seminar on New Developments in Partial Differential Equations (winter term 2013/14)

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.


SverakTopics in Mathematical Physics (lectures 29-40)http://www.math.umn.edu/~sverak/course-notes2011.pdf
BatchelorAn Introduction to Fluid DynamicsCambridge Univ. Press, 2010
YudovichUniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluidhttp://ams.mpim-bonn.mpg.de/mathscinet-getitem?mr=1312975
TurkingtonStatistical equilibrium measures and coherent states in two-dimensional turbulenceCommunications in Pure and Applied Mathematics, Vol. LII, No. 7, 1999, pp. 781-811
Majda, WangNonlinear Dynamics and Statistical Theories for Basic Geophysical FlowsSpringer, 2007
Arnold, KhesinTopological methods in hydrodynamicsSpringer, 2009
Khesin, WendtThe geometry of infinite dimensional groupsSpringer, 1999
DrazinHydrodynamic stabilityCambridge University Press, 1982
VillaniLandau dampingmain work and survey, lecture notes
Madmoudi, BedrossianInviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equationsarXiv
Lin, ZengInviscid dynamical structures near Couette flowarxiv
Li,LinA resolution of the Sommerfeld Paradoxarxiv


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
    09:00-10:00 Lukas PieronekThe Euler equation: formulations and propertiesMajda&Bertozzi (chapters 1,2.1)
    10:15-11:15Marcel GrausBeal-Kato-Majda: Well-posedness and blow-upMajda&Bertozzi, (chapters 2.5,3.3)
    11:45-12:45Lukas MatuschekWell-posedeness for L solutionsMajda&Bertozzi(chapter 8.2); Yudovich
    13:30-14:30Jan KrautterClassical stability results(Rayleigh, Fjortoft, Arnold)Drazin(section 22); Arnold&Khesin; Khesin&Wendt
  • 13.12.13
    10:15-11:15Thilo SimonConstraints and weak∗ convergenceSverak:29.2,32,33.1
    11:45-12:45Susanne GammerStatistical Mechanics and EntropySverak:31,36
    13:30-14:30Richard HöferEntropy, TurkingtonSverak;Turkington
    14:45-15:45Thomas VogtOrbits and VariationSverak:35,38 ;Turkington
  • 17.01.14
    09:00-10:00Ksenia FedosovaA variational formulation of Euler's equationArnold&Khesin
    10:30-11:30Matthäus PawelczykScattering for NLS
    11:45-12:45Marcel DenglerFree transport and linear Landau dampingVillani's script: chapter 3
    13:30-14:30Florian SchweigerLinear damping for Couette flow and behaviour of the nonlinear equationLin&Zeng
    14:45-15:45Shaoming GuoThe Sommerfeld paradoxLi&Lin
Last update: 13.01.2014 by zill