Global solutions for inhomogeneous micropolar equations with density-dependent coefficients and large data

Peng Lu; Yuanyuan Qiao; Peng Lu; Yuanyuan Qiao

doi:10.3934/era.2025336

Electronic Research Archive

2025, Volume 33, Issue 12: 7600-7618. doi: 10.3934/era.2025336

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Research article

Global solutions for inhomogeneous micropolar equations with density-dependent coefficients and large data

Peng Lu ^{1
,
,},
Yuanyuan Qiao ²

1.
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
2.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Received: 28 September 2025 Revised: 14 November 2025 Accepted: 02 December 2025 Published: 18 December 2025

In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we establish the global existence of strong solutions as long as the initial density is linearly equivalent to a large constant state. There is no restriction on the size of the initial velocity and micro-rotational velocity. As a byproduct, we prove the exponential decay for the solution.
- inhomogeneous incompressible micropolar equations,
- density-dependent coefficients,
- global strong solutions,
- large initial data,
- exponential decay
Citation: Peng Lu, Yuanyuan Qiao. Global solutions for inhomogeneous micropolar equations with density-dependent coefficients and large data[J]. Electronic Research Archive, 2025, 33(12): 7600-7618. doi: 10.3934/era.2025336

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Abstract

In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we establish the global existence of strong solutions as long as the initial density is linearly equivalent to a large constant state. There is no restriction on the size of the initial velocity and micro-rotational velocity. As a byproduct, we prove the exponential decay for the solution.

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