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Last update:
06.06.2019

 

Mathematical Aspects of Fluid Flows

May 28 - June 2, 2017, Kácov, Czech Republic



Plenary speakers

Dominic Breit
Mathematical & Computer Sciences
Mathematics
Heriot-Watt University Edinburgh
EH14 4AS
United Kingdom
Stochastic Navier-Stokes Equations

The dynamics of liquids and gases can be modeled by the Navier-Stokes system of partial differential equations describing the balance of mass and momentum in the fluid flow. In recent years their has been an increasing interest in random influences on the fluid motion modeled via stochastic partial differential equations.

In this course we will study the existence of weak martingale solutions to the stochastic Navier-Stokes equations (both incompressible and compressible). These solutions are weak in the analytical sense (derivatives exists only in the sense of distributions) and weak in the stochastic sense (the underlying probability space is not a priori given but part of the problem).

Yann Brenier
Centre de Mathématiques Laurent Schwartz
Ecole Polytechnique
91128 Palaiseau Cedex
France
Concepts of Generalized Solutions in Incompressible Fluid Mechanics

Lecture I: Measure-valued and dissipative solutions.
The concepts of measure-valued solutions and dissipative solutions were respectively introduced in the late 80s early 90s by DiPerna-Majda and Lions for the Euler equations of incompressible fluids. Although they look very different from each other, I will explain their close relationship in relation with the "weak-strong" uniqueness principle.

Lectures II and III: Variational and sharp measure-valued solutions to the Euler equations.
Using the least action principle, one may try to solve the Euler equation not as a Cauchy problem but rather as a minimization problem. This opens the way to a rather precise "sharp" concept of measure-valued solutions. Its relevence for the Cauchy problem will be discussed.

Lecture IV: Magnetic relaxation of the Euler equations and dissipative solutions.
Following K. Moffatt one can look for stationary solutions to the Euler equations with prescribed topology by solving a degenerate parabolic equations coming from MHD theory. This leads to a suitable concept of generalized solutions blending variational features with Lions' concept of dissipative solutions.

Pierre-Emmanuel Jabin
Department of Mathematics, Math Building #084
Campus Drive
University of Maryland
College Park, MD 20742-4015
USA
Quantitative Regularity Estimates for Compressible Fluids

The aim of this course is to present some of the classical and more recent techniques to control oscillations and measure the regularity of weak solutions to various models of compressible fluids and in particular: The barotropic compressible Navier-Stokes and some Navier-Stokes-Fourier systems.

We will start by introducing the regularity theory on the simpler case of linear advection equations which follows from the notion of renormalized solutions. We will then review how the estimates developed for compressible fluids, first by P.L. Lions and then by E. Feireisl for the compressible Navier-Stokes, and E. Feireisl and A. Novotny for the Navier-Stokes-Fourier system. We will finish by presenting some recent estimates introduced with D. Bresch.

Christian Rohde
Universität Stuttgart
Institut für Angewandte Analysis und numerische Simulation
Lehrstuhl für Angewandte Mathematik
Pfaffenwaldring 57
70569 Stuttgart
Germany
Diffuse Interface Modelling for Two-Phase Flow

Phase field or diffuse interface approaches are frequently used to model the complex dynamics of two-phase flow problems. The major advantage of this ansatz is the ability to describe critical phenomena like topological changes due to merging/splitting of single phases or the phases' interaction with walls. In the last years there have been substantial advancements in the theory and numerics for diffuse-interface models. The most important directions for compressible free flows will be discussed concerning well-posedness and asymptotic behaviour for various limit regimes including the classical sharp interface limit. Besides the purely analytical issues it is important that diffuse interface models allow a reliable and efficient numerical approximation. This imposes new constraints on the whole model ansatz. While there is by now a quite well-established theory for compressible free flow situations the theory for two-phase flows in porous media is still in its very beginnings. Basic new developments for least partially homogenized flow of multiple phases and components are presented.


Participants

    Main speakers

  1. Pierre-Emmanuel Jabin
  2. Yann Brenier
  3. Dominic Breit
  4. Christian Rohde
  5. Participating organizers

  6. Josef Malek
  7. Milan Pokorny
  8. Miroslav Bulicek
  9. Ondrej Kreml
  10. Michael Ruzicka
  11. Eduard Feireisl
  12. Mirko Rokyta
  13. Participants

  14. Martin Lanzendorfer
  15. Jianfeng Cheng
  16. Qin Zhang
  17. Marta Lewicka
  18. Erika Maringova
  19. Swati Sharma
  20. Vaclav Macha
  21. Pappu Kumar
  22. Sebastian Schwarzacher
  23. Franz Gmeineder
  24. Michal Bathory
  25. Martin Michalek
  26. Mikhail Turbin
  27. Aleksandr Boldyrev
  28. Simon Axmann
  29. Jan Brezina
  30. Tabea Tscherpel
  31. Anna Abbatiello
  32. Kehinde Ayodele Ajeigbe
  33. Turgut Ak
  34. Karel Tuma
  35. Kamila Lyczek
  36. Bogdan Raita
  37. Karol Hajduk
  38. Tomasz Debiec
  39. Jakub Slavik
  40. Marija Galic
  41. Petr Kaplicky
  42. Piotr Miszczak
  43. Sarka Necasova
  44. Martin Rehor
  45. Radim Hosek
  46. Pratik Nayak
  47. Matteo Caggio
  48. Martin Kalousek
  49. Jan Blechta
  50. Aneta Wróblewska-Kamiñska
  51. Ondrej Soucek
  52. Bangwei She
  53. Oldrich Ulrych
  54. Jana Peskova
  55. Hana Bilkova