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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24892 |
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| _version_ | 1866908741525307392 |
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| author | Le, Minh Cheskidov, Alexey |
| author_facet | Le, Minh Cheskidov, Alexey |
| contents | This paper studies the following chemotaxis-fluid system in a two-dimensional bounded domain $Ω$: \begin{equation*}
\begin{cases}
n_t + u \cdot \nabla n &= Δn - χ\nabla \cdot \left (n \frac{\nabla c}{c^k} \right ) + r n - \frac{μn^2}{\log^η(n+e)},
c_t + u \cdot \nabla c &= Δc - αc + βn,
u_t + u \cdot \nabla u &= Δu - \nabla P + n \nabla ϕ+ f,
\nabla \cdot u &= 0,
\end{cases} \end{equation*} where $r, μ, α, β, χ$ are positive parameters, $k, η\in (0,1)$, $ϕ\in W^{2,\infty}(Ω)$, and $f \in C^1\left(\barΩ\times [0, \infty)\right) \cap L^\infty\left(Ω\times (0, \infty)\right)$. We show that, under suitable conditions on the initial data and with no-flux/no-flux/Dirichlet boundary conditions, this system admits a globally bounded classical solution. Furthermore, the system possesses an absorbing set in the topology of $C^0(\barΩ) \times W^{1, \infty}(Ω) \times C^0(\barΩ; \mathbb{R}^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global boundedness and absorbing sets in two-dimensional chemotaxis-Navier-Stokes systems with weakly singular sensitivity and a sub-logistic source Le, Minh Cheskidov, Alexey Analysis of PDEs This paper studies the following chemotaxis-fluid system in a two-dimensional bounded domain $Ω$: \begin{equation*} \begin{cases} n_t + u \cdot \nabla n &= Δn - χ\nabla \cdot \left (n \frac{\nabla c}{c^k} \right ) + r n - \frac{μn^2}{\log^η(n+e)}, c_t + u \cdot \nabla c &= Δc - αc + βn, u_t + u \cdot \nabla u &= Δu - \nabla P + n \nabla ϕ+ f, \nabla \cdot u &= 0, \end{cases} \end{equation*} where $r, μ, α, β, χ$ are positive parameters, $k, η\in (0,1)$, $ϕ\in W^{2,\infty}(Ω)$, and $f \in C^1\left(\barΩ\times [0, \infty)\right) \cap L^\infty\left(Ω\times (0, \infty)\right)$. We show that, under suitable conditions on the initial data and with no-flux/no-flux/Dirichlet boundary conditions, this system admits a globally bounded classical solution. Furthermore, the system possesses an absorbing set in the topology of $C^0(\barΩ) \times W^{1, \infty}(Ω) \times C^0(\barΩ; \mathbb{R}^2)$. |
| title | Global boundedness and absorbing sets in two-dimensional chemotaxis-Navier-Stokes systems with weakly singular sensitivity and a sub-logistic source |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.24892 |