NEW BLOW-UP CRITERIA FOR 3D CHEMOTAXIS-NAVIER-STOKES EQUATIONS

Haoyu Wang; Yue Qu; Chenyin Qian

doi:10.11948/20210221

2022 Volume 12 Issue 1

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Haoyu Wang, Yue Qu, Chenyin Qian. NEW BLOW-UP CRITERIA FOR 3D CHEMOTAXIS-NAVIER-STOKES EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 361-377. doi: 10.11948/20210221

Citation:

Haoyu Wang, Yue Qu, Chenyin Qian. NEW BLOW-UP CRITERIA FOR 3D CHEMOTAXIS-NAVIER-STOKES EQUATIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 361-377. doi: 10.11948/20210221

NEW BLOW-UP CRITERIA FOR 3D CHEMOTAXIS-NAVIER-STOKES EQUATIONS

1.
Department of mathematics, Shanghai University, 200444 Shanghai, China
2.
Department of mathematics, Zhejiang Normal University, 321004 Jinhua, China

Corresponding author: Email address: qcyjcsx@163.com(C. Qian)
Fund Project: The authors were supported by Natural Science Foundation of Zhejiang Province (No.LY20A010017)

Abstract

Abstract

In this paper, we consider new blow-up criteria for the chemotaxis-Navier-Stokes equations in three dimensions. Specifically, by combining the Prodi-Serrin condition for oxygen concentration $\nabla c$ with some condition on the velocity or vorticity of fluid in Besov space, we establish new blow-up criteria for local existence of classical solutions for chemotaxis-Navier-Stokes equations. The scaling invariant blow-up criterion involving cell density n and gradient of velocity is also investigated.
- Chemotaxis-Navier-Stokes equations /
- blow-up criteria /
- Besov spaces.
MSC: 76D03, 35Q53, 35Q92, 92C17

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References

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