Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions

2025/06/13 by Zhongtian Hu, Hu, Zhongtian
Engineering · Materials Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Micro and Nano Robotics #Pickering emulsions and particle stabilization

paper · pdf · doi:10.48550/arxiv.2506.11414

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

In this work, we concern ourselves with the evolution of a droplet of an ideal fluid in two dimensions, which has nontrivial bulk vorticity and is only subject to the effects of surface tension. We construct initial data with initial domain being a disk and initial velocity being arbitrarily small, such that the vorticity Hessian grows exponentially infinitely in time.

Citations

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Related

• Small scale creation for solutions of the incompressible two dimensional\n Euler equation
• Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow
• A brief history of drop formation
• Regularity estimates of a fluid-free surface evolution
• Steady bubbles and drops in inviscid fluids