Наредни састанак Семинара биће одржан у четвртак, 24. октобра 2024. године, у сали 301ф Математичког института САНУ са почетком у 14.15. У питању је заједнички састанак са Одељењем за механику и Геометријским семинаром.
Предавач: Зоран Грујић, The University of Alabama at Birmingham
Наслов предавања: SPATIAL INTERMITTENCY AND TURBULENT DISSIPATION IN 3D VISCOUS AND HYPER-VISCOUS NAVIER-STOKES FLOWS
Апстракт: The problem of whether a singularity can form in an initially smooth viscous, incompressible flow described by the homogeneous (no external force) 3D Navier-Stokes (NS) equations has been a fundamental open problem in mathematical physics. A key obstacle to progress has been super-criticality of the system, i.e., there is a scaling gap between the energy level and the scaling invariant level. A manifestation of this super-criticality can be seen in the realm of the hyper-viscous flows described by the hyper-dissipative (HD) NS system. Here, the negative Laplacian is replaced by the negative Laplacian to the power (say 𝛽) greater than 1. It has been known since the fundamental work of J.L. Lions in 1960s that the HD NS system is regular for any 𝛽 greater or equal to 5/4, while what happens in the super-critical regime (1 < 𝛽 < 5/4) has remained a mystery. (At 5/4, the energy level and the scaling-invariant level coincide.)
The main goal of this lecture is to present a novel mathematical framework suitable for encoding the spatial intermittency of turbulent flows and the mechanism of turbulent dissipation for the purpose of the analysis of the possible singularity formation in the NS and HD NS flows. In particular, mathematical evidence of criticality of the NS dissipation (𝛽 = 1) will be given – namely, the approximately self-similar blow-up (a prime candidate for the formation of a singularity) is ruled out as soon as 𝛽 is greater than 1.
Напомена:
Предавање се може пратити на даљину преко линка Одељења за математику: https://miteam.mi.sanu.ac.rs/asset/WbsehnSL4ZeTPJo6r