A Beale-Kato-Majda Blow-up Criterion for a Hydrodynamic System Modeling Vesicle and Fluid Interactions

TL;DR

This paper establishes a Beale-Kato-Majda type criterion for a hydrodynamic system modeling vesicle-fluid interactions, showing that vorticity norm controls solution breakdown.

Contribution

It introduces a new blow-up criterion specific to vesicle-fluid interaction models, extending classical fluid dynamics results.

Findings

Maximum vorticity norm determines singularity formation.

The criterion applies to smooth solutions of the vesicle-fluid system.

Provides a mathematical condition for solution breakdown.

Abstract

In this paper, we establish an analog of the Beale-Kato-Majda type criterion for singularities of smooth solutions of a hydrodynamic system modeling vesicle and fluid interactions. The result shows that the maximum norm of the vorticity alone controls the breakdown of smooth solutions.