Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913179397783552 |
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| author | Wang, Wendong Wei, Dongyi Zhang, Zhifei |
| author_facet | Wang, Wendong Wei, Dongyi Zhang, Zhifei |
| contents | 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 $8π$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system Wang, Wendong Wei, Dongyi Zhang, Zhifei Analysis of PDEs 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 $8π$, 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. |
| title | Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2606.02070 |