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math.AP2026
Generic small-scale creation in the two-dimensional Euler equation
Thomas Alazard, Ayman Rimah Said
The Cauchy problem for the two-dimensional incompressible Euler equation is globally well-posed for smooth initial data. In this paper, we show that for a dense set of initia…
math.AP2025
Mixing Estimates for Passive Scalar Transport by Vector Fields
Lucas Huysmans, Ayman Rimah Said
We prove a quantitative mixing estimate for the Cauchy problem for transport along divergence-free vector fields with bounded variation. By developing a framework that quantifies A…
math.AP2024
A Unified Approach to Mixing and Regularity for Passive Scalar Transport by Sobolev Vector Fields
Lucas Huysmans, Ayman Rimah Said
We develop a new framework for quantitative estimates of passive scalar transport along Sobolev vector fields in , when . Our approach is based on Christ-Journé singu…