具有多孔介质-细胞扩散和一般灵敏度的三维趋化性Stokes系统的全局有界性

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-08-19 DOI:10.1515/anona-2022-0228

Yu Tian, Zhaoyin Xiang

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引用次数: 2

摘要

摘要在本文中，我们将发展一种分析方法来构造具有多孔介质细胞扩散Δn m\Delta｛n｝^｛m｝的三维趋化性Stokes系统初始边值问题的全局有界弱解，对于m≥65 63 m\ge\frac｛65｝｛63｝和一般灵敏度。特别是，这扩展了先前的结果，该结果断言在一般灵敏度的较大范围m>7.6 m\gt\frac｛7｝｛6｝内的全局可解性（m.Winkler，具有非线性扩散和一般灵敏度的三维趋化性Stokes系统中的有界性和大时间行为，Calc.Var.54（2015），3789–3828）或m>9 8 m\gt\frac｛9｝｛8｝的标量灵敏度（m.Winkler，具有弱强扩散增强的简并趋化性Stokes系统中的全局存在和稳定，J.Differ.Equ.264（2018），6109–6151）。我们的证明是基于对拟能量型泛函的一个新的观察和一个归纳论点。

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Global boundedness to a 3D chemotaxis-Stokes system with porous medium cell diffusion and general sensitivity

Abstract In this article, we will develop an analytical approach to construct the global bounded weak solutions to the initial-boundary value problem of a three-dimensional chemotaxis-Stokes system with porous medium cell diffusion Δ n m \Delta {n}^{m} for m ≥ 65 63 m\ge \frac{65}{63} and general sensitivity. In particular, this extended the precedent results which asserted global solvability within the larger range m > 7 6 m\gt \frac{7}{6} for general sensitivity (M. Winkler, Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity, Calc. Var. 54 (2015), 3789–3828) or m > 9 8 m\gt \frac{9}{8} for scalar sensitivity (M. Winkler, Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement, J. Differ. Equ. 264 (2018), 6109–6151). Our proof is based on a new observation on the quasi-energy-type functional and on an induction argument.

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.