Turbulent solutions of fluid equations
时间  Datetime
2023-08-13 15:00 — 16:00
地点  Venue
会议室(706)
报告人  Speaker
Alexey Cheskidov
单位  Affiliation
University of Illinois at Chicago
邀请人  Host
张登
备注  remarks
报告摘要  Abstract

In the past couple of decades, mathematical fluid dynamics has been highlighted by numerous constructions of solutions to fluid equations that exhibit pathological or wild behavior. These include the loss of the energy balance, non-uniqueness, singularity formation, and dissipation anomaly. Interesting from the mathematical point of view, providing counterexamples to various well-posedness results in supercritical spaces, such constructions are becoming more and more relevant from the physical point of view as well. Indeed, a fundamental physical property of turbulent flows is the existence of the energy cascade. Conjectured by Kolmogorov, it has been observed both experimentally and numerically, but had been difficult to produce analytically. In this talk I will overview new developments in discovering not only pathological mathematically, but also physically realistic solutions of fluid equations.
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