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

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arxiv 2404.17228 v2 pith:ZRH7EAVA submitted 2024-04-26 math.AP

classification math.AP
keywords blowupfinite-timesolutionsequationkeller-segelkeller-segel-navier-stokesnon-radialsolution
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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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  1. Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

    math.AP 2025-01 conditional novelty 8.0 of 10

    Any sufficiently small H^2 nonradial perturbation of the explicit 3D Keller-Segel self-similar blowup profile still blows up along the same self-similar profile with decaying error.

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