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arXiv · 2404.17228

Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions

Zexing Li·Tao Zhou
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Abstract

While finite-time blowup solutions have been studied in depth for the Keller-Segel equation, a fundamental model describing chemotaxis, the existence of finite-time blowup solutions to chemotaxis-fluid models remains largely unexplored. To fill this gap in the literature, we use a quantitative method to directly construct a smooth finite-time blowup solution for the Keller-Segel-Navier-Stokes system with buoyancy in 3D. The heart of the proof is to establish the non-radial finite-codimensional stability of an explicit self-similar blowup solution to 3D Keller-Segel equation with the abstract semigroup tool from [Merle-Rapha\"el-Rodnianski-Szeftel, 2022], which partially generalizes the radial stability result [Glogi\'c-Sch\"orkhuber, 2024] to the non-radial setting. Additionally, we introduce a robust localization argument to find blowup solutions with non-negative density and finite mass.

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Zexing Li, Tao Zhou. 2024-04-26. Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions. https://arxiv.org/abs/2404.17228

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