• June, 5 2024

Łukasz Mądry (...)

Title: Zero noise limit for singular ODE regularized by fractional noise

Abstract: ...

• May, 31 2024

Hakima Bessaih (...)

Title: Introduction to Data Assimilation

Abstract: ...

• May, 15 2024

Eric Simonnet (...)

Title: A Convex Integration scheme on logarithmic lattices

Abstract: The aim of this project is to build a C^beta, 0 < beta < 1/5, 3d Euler solution on logarithmic lattices. After presenting general ideas on convex integration, I will show how they can be adapted to logarithmic lattices, in particular with respect to the Nash decomposition.

This is an ongoing project with C.Campolina and W.Ruffenach.

• May, 15 2024

Ciro Campolina (...)

Title: Logarithmic lattice models for fluid flows in the presence of boundaries

Abstract: Important problems in fluid dynamics arise from the complex effects of boundaries on nonlinear multi-scale flows. In this talk, we introduce new simplified models for the study of fluid flows in the presence of solid walls. The governing equations are considered on logarithmic lattices in Fourier space, and the boundary effects are taken as localized forcing terms. The resulting models preserve the exact form of the original equations, and consequently carry over many of their core properties, like the group of symmetries, the conservation laws, and the actions of the boundaries. The fast growth rate of wavenumbers on the logarithmic lattice allows to reach impressively small scales with a reduced number of degrees of freedom. We show the potential of the proposed technique by applying it to the vanishing viscosity problem of the Navier-Stokes equations. This is a joint work with Alexei Mailybaev

• May, 15 2024

Wandrille Ruffenach (...)

Title: Anomalous diffusion by fractal homogenization: numerical investigation

Abstract: Numerical simulations of advection diffusion equation and experiments suggests that conservation of passive scalar variance is not restored upon the vanishing diffusivity limit when the advection field is a turbulent flow. No rigorous proof of this empirical fact exist but some constructions of rough turbulent-like vector fields exhibiting this behavior have been proposed throughout the years. A year ago, S. Armstrong and V. Vicol built such a vector field and proved that it produces anomalous diffusion. During my masters internship, I am exploring their construction numerically. I will give a physicist presentation of the subject and show the first numerical results.

• March, 21 2024

Maximilian Sebastian Janisch (...)

Title: Instability and non-uniqueness for the 2D Euler equations in vorticity form, after M. Vishik

Abstract: In 1963, V. Yudovich proved that weak solutions to the vorticity formulation of the 2d Euler equations are unique if the initial vorticity is chosen integrable and bounded, and if the spatial regularity of the vorticity of the weak solutions is required to remain integrable and bounded at later times. The question of whether uniqueness still holds if one replaces the boundedness condition by p-integrability for some finite p remained open until it was answered negatively by M. Vishik in 2018. In this talk, I will discuss lecture notes written by D. Albritton, E. Brué, M. Colombo, C. De Lellis, V. Giri, H. Kwon and myself, in which we explore and expand upon the approach by M. Vishik. I will discuss the non-uniqueness results as well as the idea of the proof. If time allows, I will also touch upon further developments on the non-uniqueness of Leray-Hopf solutions.

• March, 21 2024

Ruojun Huang (...)

Title: Scaling Limit for a second-order particle system with local annihilation

Abstract: We consider a simple continuum particle system written according to Newton's law with random velocity. Motivated by coagulation processes, we simplify it and consider the scenario that any pair of particles may mutually annihilate when their spatial distance are sufficiently close. As the number of particles tends to infinity and simultaneously the interaction range goes to zero, in the so-called local regime, we obtain the limit of the empirical measures on the position and velocity of active particles. The technique is inspired by Hammond and Rezakhanlou (ARMA '07), and a major role is played by the Green function of associated hypoelliptic operator.

• March, 13 2024

Marco Bagnara (Scuola Normale Superiore)

Title: Direction of vorticity and the problem of global regularity for the Navier-Stokes Equations

Abstract: ...

• March, 6 2024

Yassine Tahraoui (Scuola Normale Superiore)

Title: Introduction to Non Newtonian Differential Fluids

Abstract: ...

• March, 6 2024

Avi Mayorcas (University of Bath)

Title: Introduction and Overview to Rough Paths theory Questions and Tools

Abstract: ...

• January, 7 2024

Klas Modin (Chalmers University of Technology)

Title: The reversibility paradox in matrix hydrodynamics

Abstract: Some time ago, Milo Viviani and I unveiled numerical simulations that indicate a connection between the long-time behavior of 2-D Euler equations and integrability conditions for “blob dynamics”. After presenting these results, I was asked an insightful question: The phase space underlying the numerical model in the simulations is compact. Because the dynamics is also Hamiltonian, we have Poincaré recurrence. But the dynamics in the simulations, leading to blob formations, seem contractive. Isn't the mechanism for blob formations instead induced by fictitious dissipation, introduced via the numerical time discretization? I didn’t have a good answer at the time, but the question stayed with me. Today I have an answer, which is the subject of this talk.

• December, 13 2023 

Alessandra Lanotte (CNR-nanotech Lecce)

Title: Turbulent regime investigation in quantum fluids of light

Abstract: The observation of turbulent regimes in quantum fluids is receiving renewed interest thanks to the ability to manipulate with a high degree of control quantum systems such as superfluid helium or atomic Bose–Einstein condensates. We discuss the turbulent dynamics of a two-dimensional quantum fluid of exciton–polaritons, hybrid light–matter quasiparticles, both by measuring the kinetic energy spectrum and showing the onset of vortex clustering. These results contribute to the investigations of quantum turbulence in two-dimensional fluids, a relatively young research field.

• November, 28 2023 

Mario Maurelli (Università di Pisa)

Title: Uniqueness by Kraichnan noise for 2D Euler equations with L^p vorticity

Abstract: ....

• November, 22 2023 

Dejun Luo (Academy of Mathematics and Systems Science, CAS)

Title: Scaling limit for stochastic 2D Euler equations with transport noise and L^p (p<2) initial data.

Abstract: ....

• November, 22 2023 

Matteo Palmieri (Scuola Normale Superiore)

Title: Introduction to diffusion approximation by Homogenization Theory

Abstract: ....

• November, 15 2023 

Theresa Lange (Bielefeld University)

Title: Global Existence and non-uniqueness of 3D Euler equations perturbed by transport noise

Abstract: ....