Comprehensive Fluids, Entropy Hierarchies, and Flocking - SIAM PDE Seminar

Explore compressible fluid equations and collective dynamics in this 57-minute seminar presented by Theodore D. Drivas from Stony Brook University. Delve into Navier-Stokes models with local dissipation and nonlocal models exhibiting flocking behavior. Learn about global regularity for viscous shallow water equations and singularity formation in slender axisymmetric fluid jets. Discover a continuation criterion for smooth solutions in non-local models and the use of entropy hierarchies to control solutions. Examine how weak solutions obeying entropy inequalities demonstrate flocking behavior. Gain insights into dissipative compressible fluid models, shallow water dynamics, drop formation in liquid columns, and the mathematical description of flocking through the Continuum Cucker-Smale model.

Intro
10 Dissipative Compressible Fluid Models
dynamics of shallow water
10 Shallow water
Drop formation in liquid columns
Slender jet equations
Flocking and emergent organization
Continuum Cucker Smale model
Mathematical description of flocking
Transport Structure of Dissipation
First-order Entropies
Proof of Flocking