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Global existence of the strong solution to the 3D incompressible micropolar equations with fractional partial dissipation

Part of: Incompressible inviscid fluids Incompressible viscous fluids

Published online by Cambridge University Press:  13 September 2022

Yujun Liu Open the ORCID record for Yujun Liu [Opens in a new window]
Yujun Liu*
Affiliation:
Department of Mathematics and Computer, Panzhihua University, Panzhihua 617000, P. R. China
*
e-mail: liuyujun6@126.com
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Abstract

In this paper, we considered the global strong solution to the 3D incompressible micropolar equations with fractional partial dissipation. Whether or not the classical solution to the 3D Navier–Stokes equations can develop finite-time singularity remains an outstanding open problem, so does the same issue on the 3D incompressible micropolar equations. We establish the global-in-time existence and uniqueness strong solutions to the 3D incompressible micropolar equations with fractional partial velocity dissipation and microrotation diffusion with the initial data $(\mathbf {u}_0,\ \mathbf {w}_0)\in H^1(\mathbb {R}^3)$.

Keywords

Incompressible micropolargractionalpartial dissipation

MSC classification

Primary: 76B03: Existence, uniqueness, and regularity theory 76D03: Existence, uniqueness, and regularity theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 75 , Issue 5 , October 2023 , pp. 1516 - 1539
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

Liu is supported by the Panzhihua University Foundation (Grant No. 035200075).

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