Small scales and singularity formation in fluid dynamics

TL;DR

This paper reviews recent progress in understanding how singularities and small-scale structures develop in solutions to fluid dynamics equations, focusing on Euler and SQG models.

Contribution

It synthesizes recent advances in the study of singularity formation and small scales in fluid dynamics equations, highlighting key theoretical developments.

Findings

Insights into conditions leading to singularities in Euler and SQG equations

Identification of mechanisms driving small-scale formation in fluid flows

Summary of recent mathematical techniques used in the analysis

Abstract

We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.