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Geometrical and statistical fluid dynamics: October 11-17, 2017

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Organized by: Uriel Frisch, Konstantin Khanin and Rahul Pandit

Some of the most basic questions relating to the Euler and Navier-Stokes equations for the motion of a 3D incompressible fluid are still open. There is a strong belief that answers to these questions cannot be obtained without creative use of geometric/Lagrangian and measure-theoretic/probabilistic tools. This is the purpose of the present workshop. It will bring together two communities – mathematicians and physicists/numericists – and will establish a common language that allows them to work together on these questions.

On the mathematical side, the emphasis will be on geometrical and statistical/stochastic methods to tackle both continuous and discrete versions of hydrodynamics.

On the physical and computational side, the novelty is, to a large extent, the realization that Lagrangian methods – where one follows fluid particles – give us much more geometric and dynamic insight than, so-called, Eulerian ones.

In recent years there has been a strong renewal of interest in the Lagrangian description of flows. It was shown that the Cauchy invariants can be used to develop highly efficient Cauchy-Lagrangian numerical schemes for the Euler equation with or without boundaries. Such schemes completely bypass the usual Courant-Friedrichs-Lewy condition on the size of time steps and thus can be orders of magnitude faster than Eulerian methods.

Turbulent flow, in the limit of large Reynolds numbers, may be viewed as weak dissipative solutions of the Euler equations. There has been much progress recently regarding the Eulerian description of such flow.

There has been an important recent development in the theory of stochastic PDEs with highly singular forcing and thus very rough paths, such as the Kardar-Parisi-Zhang (KPZ) problem. It is of considerable interest to try to apply such ideas to genuine hydrodynamical problems.

Revisiting the mathematical foundations of fluid evolution models. For example, a fundamental geometrical and measure-theoretical question can now be addressed: what is the structure of arbitrary large compositions of arbitrary small action incompressible (measure-preserving) motions without any further regularity assumptions?

This workshop is also associated with the program: Geometrical and statistical fluid dynamics.

Talk Schedule


Time Title Presenter Location
10:00am The Onsager 1/3 rule in a bounded domain Bardos, Claude SCGP 102
10:45am Coffee break N/A SCGP Cafe
11:15am Weak vorticity formulation for incompressible 2D Euler in domains with boundary Nussenzveig, Lopes Helena SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:30pm Remarks on high Reynolds number hydrodynamics Constantin, Peter SCGP 102
2:15pm Onsager conjecture and beyond Buckmaster, Tristan SCGP 102
3:00pm Coffee Break N/A SCGP Cafe
3:30pm N/A Discussion Session SCGP 102

Time Title Presenter Location
10:00am A scaling law for Kolmogorov 1962 and corrections to the log normal hypothesis Glimm, James SCGP 102
10:45am Coffee break N/A SCGP Cafe
11:15am Turbulent mixing and generalized flows Bec, Jeremie SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:30pm Lagrangian power statistics and irreversibility in turbulence Biferale, Luca SCGP 102
2:15pm Thermalization in hydrodynamical systems Brachet, Marc SCGP 102
3:00pm Coffee Break N/A SCGP Cafe

Time Title Presenter Location
10:00am Exact solutions of the stochastic Burgers equation Spohn, Herbert SCGP 102
10:45am Coffee break N/A SCGP Cafe
11:15am A stochastically forced shell model of turbulence Friedlander, Susan SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:30pm Inviscid limit for the Rayleigh-Taylor instability as a spontaneously stochastic dynamics Mailybaev, Alexei SCGP 102
2:15pm Stochastic Lagrangian Representation of Diffusion and Dissipation in Fluid Dynamics Eyink, Greg SCGP 102
3:00pm Coffee Break N/A SCGP Cafe
3:30pm N/A Discussion Session SCGP 102
6:00pm N/A Banquet SCGP Cafe

Time Title Presenter Location
10:00am Serfati’s method for Lagrangian time analyticity Hertel, Tobias SCGP 102
10:45am Coffee break N/A SCGP Cafe
11:15am Regularity of Lagrangian incompressible Euler flow in a bounded domain Besse, Nicolas SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:30pm Geometry of motion of vortex sheets Khesin, Boris SCGP 102
2:15pm D’Alembert Principle, Weak Solutions of the Euler Equations, and Turbulence Shnirelman, Alexander SCGP 102
3:00pm Coffee Break N/A SCGP Cafe
3:30pm N/A Discussion Session SCGP 102

Time Title Presenter Location
10:00am Large events in turbulence at very large Reynolds numbers Pumir, Alain SCGP 102
10:45am Coffee break N/A SCGP Cafe
11:15am The effects of the negative curvature on the Navier-Stokes equations Czubak, Magdalena SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:30pm Stochastic 3D Navier-Stokes Equations + Waves: Averaging, Convergence and Regularity Mahalov, Alex SCGP 102
2:15pm Hydrodynamics via combinatorial topology Sullivan, Dennis SCGP 102
3:00pm Coffee Break N/A SCGP Cafe
3:30pm N/A Discussion Session SCGP 102


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