The next meeting of “Fudan International Seminar on Analysis, PDEs, and Fluid Mechanics” will take place on Thursday, November 7, 2024.
The next talk: Professor Filippo Gazzola (Politecnico di Milano)
Title of the talk: “New tools for detecting the epochs of irregularity of Leray-Hopf solutions to some 3D Navier-Stokes equations”
Time: Thursday, 7 of November, 21:00 - 22:00 (Shanghai time), 14:00 - 15:00 (Rome and Paris time), 13:00 -14:00 (London time), 15:00 - 16:00 (Vilnius and Tel-Aviv time), 8:00-- 9:00 a.m. (US ET), 10:00--11:00 a.m. (Chile Santiago time).
Abstract:
We study global Leray-Hopf solutions to Cauchy problems for the 3D Navier-Stokes equations in a cube under Navier boundary conditions. With a suitable reflection procedure, these solutions become space-periodic over the whole space R^3.
Since the pioneering work by Jean Leray, it is known that solutions exist for any initial data with finite energy but it is not known whether their enstrophy may blow up in finite time in the so-called epochs of irregularity. Our simplified geometric and functional-analytic framework enables us to determine explicit bounds both for the epochs of irregularity and for the enstrophy. By using this information we bring strong evidence that the enstrophy blow-up may indeed occur in finite time due to the energy equipartition among the Fourier components of the solution to a finite-dimensional Galerkin approximation of the problem. This is a joint work with Gianni Arioli and Alessio Falocchi.
ZOOM link: https://us02web.zoom.us/j/83673138944?pwd=azQyc1BwUjJFY3VjMStLbFR5Z2VwUT09
ZOOM Id: 836 7313 8944
Passcode: 808818
We are pleased to inform you that the information on previous talks is available on the seminar web page
https://researchseminars.org/seminar/Cafe_Analysis_and_Fluid
see PastTalks section
We sincerely hope you will be able to participate.