Global Solvability for 3D Incompressible Inhomogeneous Micropolar System in Critical Spaces

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-07-24 DOI:10.1111/sapm.70086

Yelei Guo, Chenyin Qian, Ting Zhang, Xiaole Zheng

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Abstract

In this paper, we investigate the 3D inhomogeneous incompressible micropolar system with the initial density $ρ_{0}$ being discontinuous and the initial velocity $(u_{0}, ω_{0})$ possessing critical regularity. Assuming that $ρ_{0}$ is close to a positive constant, we obtain the global existence and uniqueness of the solution if $(u_{0}, ω_{0})$ is small in ${\dot{B}}_{p, 1}^{- 1 + 3 / p} (R^{3}) (1 < p < 3)$ . The key ingredient in the proof lies in a new maximal regularity estimate for the generalized heat equation in Lorentz space. Our result corresponds to the interesting results established by Danchin and Wang [Communications in Mathematical Physics, 2023] for 3D inhomogeneous incompressible Navier–Stokes equations. Besides, the uniqueness of the Fujita–Kato-type solution for the micropolar fluids constructed by Qian, Chen, and Zhang [Mathematische Annalen, 2023] is also established.

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临界空间中三维不可压缩非齐次微极系统的全局可解性

本文研究了三维非均匀不可压缩微极系统，初始密度ρ 0 $\rho _0$不连续，初始速度(u 0，ω 0) $(u_0,\omega _0)$具有临界规律性。假设ρ 0 $\rho _0$接近于一个正常数，我们得到解的整体存在唯一性，如果(u 0，ω 0) $(u_0,\omega _0)$在B * p中较小；1−1 + 3 / p （R 3）(1 ＆lt；P ＆lt；3) $\dot{B}^{-1+3/p}_{p,1}(\mathop {\mathbb {R}\hspace{0.0pt}}\nolimits ^3)(1<p<3)$。证明的关键在于对洛伦兹空间中广义热方程的一个新的极大正则性估计。我们的结果与Danchin和Wang [Communications in Mathematical Physics， 2023]建立的3D非齐次不可压缩Navier-Stokes方程的有趣结果相对应。此外，还建立了Qian、Chen和Zhang [Mathematische Annalen， 2023]构建的微极流体的fujita - kato型解的唯一性。

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.