Global boundedness in a Chemotaxis-May-Nowak model for virus dynamics with logistic damping
Abstract
This paper investigates the following May--Nowak type model for viral infection in a bounded domain Ω⊂ ℝn, n ≥ 2: ut = Δu − χ∇ · (u ∇ v) + κ− u − uw − μ(u1+α)/(lnk(u+e)), [1mm] γvt = Δv − v + uw, [1mm] wt = Δw − w + v, where χ∈ ℝ, μ> 0, k ∈ [0,1), α> 0, and γ∈ {0,1}. We establish the global existence and uniform-in-time boundedness of classical solutions for suitably regular initial data under one of the following conditions: (A) γ= 1, n = 2, k ∈ [0,1), α= 1, and μ> 0; (B) γ= 1, 3 ≤ n ≤ 5, k = 0, α= 1, and μ is sufficiently large; (C) γ= 1, n ≥ 6, k = 0, α> (n−2)/4, and μ> 0; (D) γ= 0, n ≥ 2, k = 0, α> (n+2)/2, and μ>0. In particular, in the physically relevant dimensions n = 2,3, both subquadratic and quadratic damping are sufficient to prevent blow-up. Moreover, in the fully parabolic case (γ= 1), our results improve upon recent findings by relaxing the condition α> n/2 to weaker assumptions within the above parameter regimes.
Related
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BibTeX
@misc{le2026global,
title = {{Global boundedness in a Chemotaxis-May-Nowak model for virus dynamics with logistic damping}},
author = {Minh Le},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29134},
eprint = {2609.29134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29134},
}
RIS
TY - UNPB
TI - Global boundedness in a Chemotaxis-May-Nowak model for virus dynamics with logistic damping
AU - Minh Le
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29134
UR - https://arxiv.org/abs/2609.29134
AB - This paper investigates the following May--Nowak type model for viral infection in a bounded domain Ω⊂ ℝ^n, n ≥ 2: u_t = Δu − χ∇ · (u ∇ v) + κ− u − uw − μ(u^1+α)/(ln^k(u+e)), [1mm] γv_t = Δv − v + uw, [1mm] w_t = Δw − w + v, where χ∈ ℝ, μ> 0, k ∈ [0,1), α> 0, and γ∈ {0,1}. We establish the global existence and uniform-in-time boundedness of classical solutions for suitably regular initial data under one of the following conditions: (A) γ= 1, n = 2, k ∈ [0,1), α= 1, and μ> 0; (B) γ= 1, 3 ≤ n ≤ 5, k = 0, α= 1, and μ is sufficiently large; (C) γ= 1, n ≥ 6, k = 0, α> (n−2)/4, and μ> 0; (D) γ= 0, n ≥ 2, k = 0, α> (n+2)/2, and μ>0. In particular, in the physically relevant dimensions n = 2,3, both subquadratic and quadratic damping are sufficient to prevent blow-up. Moreover, in the fully parabolic case (γ= 1), our results improve upon recent findings by relaxing the condition α> n/2 to weaker assumptions within the above parameter regimes.
ER -