Analysis and Applied Mathematics Seminar
Alexey Cheskidov
Westlake University
Energy cascade in fluids: from convex integration to mixing
Abstract: In the past couple of decades, mathematical fluid dynamics has
made significant strides with numerous constructions of solutions to fluid
equations that exhibit pathological or wild behaviors. 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.
Monday May 5, 2025 at 12:00 PM in 636 SEO