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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.07982 |
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| _version_ | 1866917691599618048 |
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| author | Ding, Mengyao Fang, Yuzhou Zhang, Chao |
| author_facet | Ding, Mengyao Fang, Yuzhou Zhang, Chao |
| contents | In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented here has broad applications in determining large time behaviours of weak solutions and improving the regularity for models involving the $p$-Laplace operator. To demonstrate the applicability of our findings, we investigate the asymptotic stability of a chemotaxis model with nonlinear signal production and a chemotaxis-Navier-Stokes model with a logistic source. Additionally, within the context of $p$-Laplacian diffusion, we establish Hölder continuity for a chemotaxis-haptotaxis model and a chemotaxis-Stokes model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative analysis and its applications for Keller-Segel type systems Ding, Mengyao Fang, Yuzhou Zhang, Chao Analysis of PDEs In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented here has broad applications in determining large time behaviours of weak solutions and improving the regularity for models involving the $p$-Laplace operator. To demonstrate the applicability of our findings, we investigate the asymptotic stability of a chemotaxis model with nonlinear signal production and a chemotaxis-Navier-Stokes model with a logistic source. Additionally, within the context of $p$-Laplacian diffusion, we establish Hölder continuity for a chemotaxis-haptotaxis model and a chemotaxis-Stokes model. |
| title | Quantitative analysis and its applications for Keller-Segel type systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.07982 |