Turb1d 2021

The Universidad de Cantabria (UC), the Centro Internacional de Encuentros Matemáticos (CIEM) and the Institute Camille Jordan (ICJ) are organizing an online conference on the study of mathematical models of turbulence and related phenomena. The conference will take place in Santander.

Schedule

  • Tuesday 2nd November, 13:00-15:00 Welcome Lunch at Cafetería Escudero

  • Tuesday 2nd November, 15h00 - 16h00 (central EU time): Luis Vega (UPV-EHU and BCAM);
    Title: TBA
    Abstract: TBA

  • Tuesday 2nd November, 16h00 - 17h00 (central EU time): Amina Mecherbet (IMJ-PRG);
    Title:     Homogenization of Stokes equations with randomly rotating particles
    Abstract:     This talk is dedicated to the rigorous derivation of a fluid-kinetic model describing suspension of rod-like particles in a viscous fluid starting from a microscopic description. The limit model is known as the Doi model and corresponds to a Stokes equation for the fluid velocityand a Fokker-Planck (Smoluchowski) equation for the probability distribution of the rod positions and orientations in time. I will first present the main results for the derivation of kinetic equations for sedimentation of inertialess spherical particles in a viscous fluid using homogenization techniques and a mean field approach. Second I will explain the main difficulties encountered when considering rod like particles and present the simplified model considered in order to perform a homogenization process. The toy model encodes the main ingredients in order to justify rigorously the appearance of the so called viscoelastic stress term in the Doi model.This talk is based on an ongoing work with Richard H\"ofer and Marta Leocata.

  • Tuesday 2nd November, 17h00 - 17h30 (central EU time): Coffee Break by Cafetería de Ciencias

  • Tuesday 2nd November, 17h30 - 18h30 (central EU time): Luigi Berselli (Universitá di Pisa);
    Title:     On the unsteady rotational Smagorinsky (Baldwin-Lomax) model
    Abstract:     We show that the rotational Smagorinsky model for turbulent flows can be put in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions identifying a proper weighted spaces and checking some easily verifiable assumptions, at fixed time. We also will briefly discuss the critical role of the exponents present in the model (power of the distance function and power of the curl)



  • Wednesday 3rd November, 09h00 - 10h00 (central EU time): Lorenzo Brandolese (ICJ);
    Title:     Forcing rapid dissipation of Navier-Stokes flows
    Abstract:     A rapidly dissipative Navier-Stokes flow in R^3 is a solution such the energy decays faster than Wiegner's critical decay rate t^{-5/2}. We provide an algorithm that, for any sufficiently localised, small initial data, explicitly constructs an external force with compact-support in space-time, such that the corresponding solution is rapidly dissipative. This is a joint work with Takahiro Okabe (Osaka).

  • Wednesday 3rd November, 10h00 - 11h00 (central EU time): Charlotte Perrin (CNRS);
    Title:     Traveling waves for the porous medium equation in the incompressible limit
    Abstract:     In this talk, I will introduce a one-dimensional porous medium equation modeling the growth of living tissues. I will analyze the behavior and the stability of traveling waves solutions to this model in the so-called "incompressible limit". In this asymptotics, the pressure, which governs the diffusion process and limits the creation of cells in the tissue, becomes very stiff and the original PDE degenerates towards a free boundary problem of Hele-Shaw type. This is a joint work with Anne-Laure Dalibard and Gabriela Lopez-Ruiz.

  • Wednesday 3rd November, 11h00 - 11h30 (central EU time): Coffee Break by Cafetería de Ciencias

  • Wednesday 3rd November, 11h30 - 12h30 (central EU time): Christian Zillinger (KIT);
    Title:     On traveling waves and echo chains in the Boussinesq equations
    Abstract:     The 2D Boussinesq equations describe the evolution of a heat conducting viscous fluid. In this talk I show that in the setting without thermal dissipation there exist explicit non-trivial traveling wave solutions near shear flows and hydrostatic balance. Moreover, the linearized equations around these waves exhibit resonances, called echoes, despite viscous dissipation of the velocity. There is a critical Gevrey 3 regularity class for which infinitely many resonances cause the temperature and vorticity to diverge to infinity in Sobolev regularity as $t\rightarrow \infty$. Yet, convergence of the velocity may persist despite this blow-up.

  • Wednesday 3rd November, 12h30 - 14h30 (central EU time): Lunch at Cafetería Escudero

  • Wednesday 3rd November, 14h30 - 15h30 (central EU time): Christophe Prange (Cergy Paris Université);
    Title:     Quantitative regularity for the Navier-Stokes equations via spatial concentration
    Abstract:     This talk is concerned with the regularity of solutions to the three-dimensional Navier-Stokes equations under boundedness of certain critical or slightly supercritical norms. I will explain recent ideas to quantify explicitly some regularity criteria. One of the keys is to study the concentration of specific critical quantities. This is joint work with Tobias Barker (University of Bath).

  • Wednesday 3rd November, 15h30 - 16h30 (central EU time): Angel Castro (ICMAT);
    Title:     TBA
    Abstract: TBA



Organizers: Francesco Fanelli (ICJ) and Rafael Granero-Belinchón (UC).