Improved Global Boundedness Criteria via Refined Bootstrap Estimates for a Quasilinear Chemotaxis-May-Nowak System
Abstract
We study a quasilinear chemotaxis--May--Nowak system with nonlinear diffusion growing at least as sm−1 at high densities and derive improved criteria for global existence and uniform boundedness. For the parabolic--elliptic--parabolic system, we establish global boundedness when m>3−4/n for n∈{2,3} and when m>1+n/4 for n≥4. For the fully parabolic system, the same conclusion holds under m>1+n/4 for n≥4. The proof relies on two refined estimates. Weighted space--time control of the nonlinear infection source yields the low-order Lq-bounds for the free virus density needed to initiate the bootstrap in the parabolic--elliptic--parabolic case. Subsequently, preserving the product structure of this source in the interpolation argument allows the chemotactic contribution to be absorbed more efficiently by the nonlinear diffusion. These estimates improve the previously known sufficient conditions for global boundedness.
Related
- Global Boundedness and Finite-Time Blow-up for a Quasilinear Chemotaxis--May--Nowak System
- A SHARP MASS THRESHOLD FOR BOUNDEDNESS IN A CRITICAL QUASILINEAR CHEMOTAXIS MODEL WITH INDIRECT SIGNAL PRODUCTION: THE RADIALLY SYMMETRIC CASE
- Global boundedness in a Chemotaxis-May-Nowak model for virus dynamics with logistic damping
- Boundedness in a chemotaxis system with nonlinear diffusion and singular sensitivity
- Chemotaxis-Stokes system with p-Laplacian slow diffusion: global boundedness across the full p>2 range
BibTeX
@misc{bai2026improved,
title = {{Improved Global Boundedness Criteria via Refined Bootstrap Estimates for a Quasilinear Chemotaxis-May-Nowak System}},
author = {Xueli Bai and Fang Li and Suying Liu and Xuxuan Luo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33657},
eprint = {2610.33657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33657},
}
RIS
TY - UNPB
TI - Improved Global Boundedness Criteria via Refined Bootstrap Estimates for a Quasilinear Chemotaxis-May-Nowak System
AU - Xueli Bai
AU - Fang Li
AU - Suying Liu
AU - Xuxuan Luo
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33657
UR - https://arxiv.org/abs/2610.33657
AB - We study a quasilinear chemotaxis--May--Nowak system with nonlinear diffusion growing at least as s^m−1 at high densities and derive improved criteria for global existence and uniform boundedness. For the parabolic--elliptic--parabolic system, we establish global boundedness when m>3−4/n for n∈{2,3} and when m>1+n/4 for n≥4. For the fully parabolic system, the same conclusion holds under m>1+n/4 for n≥4. The proof relies on two refined estimates. Weighted space--time control of the nonlinear infection source yields the low-order L^q-bounds for the free virus density needed to initiate the bootstrap in the parabolic--elliptic--parabolic case. Subsequently, preserving the product structure of this source in the interpolation argument allows the chemotactic contribution to be absorbed more efficiently by the nonlinear diffusion. These estimates improve the previously known sufficient conditions for global boundedness.
ER -