Analysis of Fluid Equations at Bath                 

Abstracts

Thierry Gallay: Mixing in shear flows, from enhanced dissipation to Taylor dispersion 

We consider the long-time dynamics of a passive scalar advected by a shear flow in an infinite cylinder, in any space dimension. Under generic assumptions on the shear velocity, we obtain optimal decay estimates both in the enhanced dissipation regime, where the diffusivity is small compared to the streamwise wave number, and in the converse regime where Taylor dispersion occurs. Our results are most conveniently established using resolvent estimates, but can also be obtained, at least in some particular situations, via the hypocoercivity method. This talk is based on joint work with Michele Coti Zelati (Imperial College, London). 

Monica Musso: Long time behavior for vortex dynamics in the 2 dimensional Euler equations 

The evolution of a two dimensional incompressible ideal fluid with smooth initial  vorticity concentrated in small regions is well understood on finite intervals of time: it converges to a super position of Dirac deltas centered at collision-less solutions to the point vortex system, in the limit of vanishing regions. Even though  for generic initial conditions the vortex point system has a global smooth solution, much less is known on the long time behavior of the fluid vorticity.

We consider the case of two vortex pairs traveling in opposite directions. Using gluing methods we describe the global dynamics of this configuration. This work is in collaboration with J Davila (U. of Bath), M. del Pino (U of Bath) and S. Parmeshwar (Imperial College London).

Emil Wiedemann: Strong Convergence of Vorticity in the Vanishing Viscosity Limit 

The two-dimensional homogeneous incompressible Euler equations possess a beautiful transport structure which gives rise to useful a priori estimates for the vorticity of the flow. In the absence of physical boundaries, it is standard to show that, as viscosity tends to zero, the vorticities associated with the Navier-Stokes equations converge weakly along a subsequence to the vorticity of an Euler flow. We show that this convergence can be upgraded to strong in three situations: 2D flows with periodic boundary condition, 3D axisymmetric flows, and, under additional assumptions, 2D flows on bounded domains.  

Tobias Barker: Remarks on Onsager Supercritical '2.75' Shear Flows

I will briefly remark on the inviscid limit in the context of 2.75 shear flows, belonging to Onsager supercritical spaces. Joint work with Christophe Prange (Cergy) and Jin Tan (Cergy). 

Contact

Tobias Barker 

''firstname''barker5 (youknowwhattoput)gmail(dot)com