Regularity and drift by Osgood vector fields

TL;DR

This paper studies how regularity is lost or maintained in transport equations driven by Osgood vector fields and applies these findings to derive stability estimates for 2D Euler equations with generalized initial data.

Contribution

It introduces new regularity and stability results for transport equations with Osgood vector fields, extending understanding of fluid dynamics models.

Findings

Quantitative stability estimate for 2D Euler with generalized Yudovich data

Analysis of regularity propagation in transport equations with Osgood vector fields

Insights into the behavior of solutions under irregular vector fields

Abstract

We consider the problem of loss and propagation of regularity of transport equation with Osgood vector field. As an application, we obtain a quantitative stability estimate for 2D incompressible Euler equation with generalized Yudovich initial data.