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Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system
[Submitted on 1 Jun 2026] · 2026-06-02 · via math updates on arXiv.org

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Abstract:In this paper, we investigate critical mass threshold for the Patlak-Keller-Segel-Navier-Stokes system on the two-dimensional whole space and obtain global existence of strong solutions if the initial mass is less than or equal to $8\pi$, regardless of the initial norm of the velocity. One new observation is that the local mass of the density function rearrangement satisfies a good inequality that is independent of velocity; and then an improved maximum principle is applied by choosing a nice auxiliary function.

Submission history

From: Wendong Wang [view email]
[v1] Mon, 1 Jun 2026 10:59:56 UTC (22 KB)