Partial regularity of solutions to the 3D chemotaxis-Navier-Stokes equations at the first blow-up time

2022/07/11 by Xiaomeng Chen, Shuai Li, Chen, Xiaomeng +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Micro and Nano Robotics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2207.04870

openalex publication_date 2022/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we investigate partial regularity of weak solutions of the three dimensional chemotaxis-Navier-Stokes equations, and obtain the \frac53-dimensional Hausdorff measure of the possible singular set is vanishing at the first blow-up time. The new ingredients are to establish certain type of local energy inequality and deal with the non-scaling invariant quantity of nln n, which seems to be the first description for the singular set of weak solutions of the chemotaxis-fluid model, which is motivated by Caffarelli-Kohn-Nirenberg's partial regularity theory \citeCKN.

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