Details
| Original language | English |
|---|---|
| Pages (from-to) | 5177-5202 |
| Number of pages | 26 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 28 |
| Issue number | 10 |
| Early online date | Dec 2022 |
| Publication status | Published - Oct 2023 |
Abstract
We consider the system (Formula presented), in smooth bounded domains Ω ⊂ RN, N ∈ N, for given f ≥ 0, φ and complemented with initial and homogeneous Neumann–Neumann–Dirichlet boundary conditions, which models aerobic bacteria in a fluid drop. We assume f(0) = 0 and f0(0) = 0, that is, that f decays slower than linearly near 0, and construct global generalized solutions provided that either N = 2 or N > 2 and no fluid is present. If additionally N = 2, we next prove that this solution eventually becomes smooth and stabilizes in the large-time limit. We emphasize that these results require smallness neither of χ nor of the initial data.
Keywords
- Chemotaxis, eventual smoothness, fluid, generalized solutions, logarithmic sensitivity
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Discrete and Continuous Dynamical Systems - Series B, Vol. 28, No. 10, 10.2023, p. 5177-5202.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Chemotaxis(-Fluid) Systems With Logarithmic Sensitivity And Slow Consumption
T2 - Global Generalized Solutions And Eventual Smoothness
AU - Fuest, Mario
N1 - Funding Information: The author would like to thank the Max Planck Institute for Mathematics in the Sciences for providing access to the article [6].
PY - 2023/10
Y1 - 2023/10
N2 - We consider the system (Formula presented), in smooth bounded domains Ω ⊂ RN, N ∈ N, for given f ≥ 0, φ and complemented with initial and homogeneous Neumann–Neumann–Dirichlet boundary conditions, which models aerobic bacteria in a fluid drop. We assume f(0) = 0 and f0(0) = 0, that is, that f decays slower than linearly near 0, and construct global generalized solutions provided that either N = 2 or N > 2 and no fluid is present. If additionally N = 2, we next prove that this solution eventually becomes smooth and stabilizes in the large-time limit. We emphasize that these results require smallness neither of χ nor of the initial data.
AB - We consider the system (Formula presented), in smooth bounded domains Ω ⊂ RN, N ∈ N, for given f ≥ 0, φ and complemented with initial and homogeneous Neumann–Neumann–Dirichlet boundary conditions, which models aerobic bacteria in a fluid drop. We assume f(0) = 0 and f0(0) = 0, that is, that f decays slower than linearly near 0, and construct global generalized solutions provided that either N = 2 or N > 2 and no fluid is present. If additionally N = 2, we next prove that this solution eventually becomes smooth and stabilizes in the large-time limit. We emphasize that these results require smallness neither of χ nor of the initial data.
KW - Chemotaxis
KW - eventual smoothness
KW - fluid
KW - generalized solutions
KW - logarithmic sensitivity
UR - http://www.scopus.com/inward/record.url?scp=85163283614&partnerID=8YFLogxK
U2 - /10.48550/arXiv.2211.01019
DO - /10.48550/arXiv.2211.01019
M3 - Article
AN - SCOPUS:85163283614
VL - 28
SP - 5177
EP - 5202
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 10
ER -