Well-posedness for heat conducting non-Newtonian micropolar fluid equations

Changjia Wang; Yuxi Duan; Changjia Wang; Yuxi Duan

doi:10.3934/era.2024043

Electronic Research Archive

2024, Volume 32, Issue 2: 897-914. doi: 10.3934/era.2024043

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Research article

Well-posedness for heat conducting non-Newtonian micropolar fluid equations

Changjia Wang ^,,
Yuxi Duan

School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China

Received: 11 October 2023 Revised: 28 December 2023 Accepted: 05 January 2024 Published: 15 January 2024

In this paper, we consider the first boundary value problem for a class of steady non-Newtonian micropolar fluid equations with heat convection in the three-dimensional smooth and bounded domain $ \Omega $. By using the fixed-point theorem and introducing a family of penalized problems, under the condition that the external force term and the vortex viscosity coefficient are appropriately small, the existence and uniqueness of strong solutions of the problem are obtained.
- non-Newtonian fluid,
- micropolar fluid,
- heat convection,
- strong solutions,
- existence and uniqueness
Citation: Changjia Wang, Yuxi Duan. Well-posedness for heat conducting non-Newtonian micropolar fluid equations[J]. Electronic Research Archive, 2024, 32(2): 897-914. doi: 10.3934/era.2024043

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Abstract

In this paper, we consider the first boundary value problem for a class of steady non-Newtonian micropolar fluid equations with heat convection in the three-dimensional smooth and bounded domain $ \Omega $. By using the fixed-point theorem and introducing a family of penalized problems, under the condition that the external force term and the vortex viscosity coefficient are appropriately small, the existence and uniqueness of strong solutions of the problem are obtained.

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