Mathematics

CLC number: O175.2

Global Strong Solutions to a Two-Dimensional Keller-Segel-Navier-Stokes System with Subcritical Sensitivity

具有次临界敏感性的二维Keller-Segel-Navier-Stokes方程组的强解的整体存在性

¹ Department of Mathematics and Physics, Sanjiang University, Nanjing 210012, Jiangsu, China (三江学院　数理部，江苏　南京　210012)
² School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, Jiangsu, China (南京航空航天大学　数学学院，江苏　南京　211106)
³ School of Mathematics and Big Data, Chaohu University, Hefei 238000, Anhui, China (巢湖学院　数学与大数据学院，安徽　合肥　238000)
⁴ School of Mathematics, Southeast University, Nanjing 211189, Jiangsu, China (东南大学　数学学院，江苏　南京　211189)

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 November 2025

Abstract

In this paper, we prove the global existence of strong solutions to a two-dimensional (2D) Keller-Segel-Navier-Stokes system with subcritical sensitivity in a bounded domain. Using energy methods, interpolation inequalities and the Gronwall lemma, we establish uniform a priori estimates for the solutions. We prove the existence and uniqueness of global strong solutions under appropriate initial conditions, along with higher-order Sobolev regularity of solutions. The result extends existing conclusions and enriches the global well-posedness theory for chemotaxis-fluid coupled models.

摘要

本文证明了有界区域中一类带次临界敏感性的二维 Keller-Segel-Navier-Stokes 系统强解的整体存在性。利用能量方法、插值不等式及 Gronwall 引理，我们建立了解的一致先验估计。在适当的初值条件下，证明了该系统整体强解的存在唯一性，并得到了解的高阶 Sobolev 正则性。该结果推广了已有的结论，丰富了趋化–流体耦合模型的整体适定性理论。