Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.17186 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we consider the following parabolic-parabolic-elliptic system } \begin{align*} \left\{\aligned & u_t=Δu-\nabla\cdot(u\nabla v)+ξ\nabla\cdot(u\nabla w)+au-μu^α, && x\inΩ, t>0,\\ & v_t=Δv+\nabla\cdot(v\nabla w)-v+u,&& x\inΩ, t>0,\\ & 0=Δw-w+u,&& x\inΩ, t>0\\ \endaligned\right. \end{align*} on a bounded domain $Ω\subset \mathbb{R}^{N}$ ($N\geq1$) with smooth boundary $\partial Ω$, where $μ$, $a$, $α$ are positive constants and $ξ\in\mathbb{R}$. If one of the following cases holds:\\ (i) $N\geq4$ and $α>\frac{4N-4+N\sqrt{2N^2-6N+8}}{2N}$;\\ (ii) $N=3$, $α>2$, for any $μ>0$ or $α=2$, the index $μ$ should be suitably big;\\ (iii) $N=2$, $α\geq2$, for any $μ>0$.\\ Without any restriction on the index $ξ$, for any given suitably regular initial data, the corresponding Neumann initial-boundary problem admits a unique global and bounded classical solution.