Improved Global Boundedness Criteria via Refined Bootstrap Estimates for a Quasilinear Chemotaxis-May-Nowak System
Year: 2026
Type: preprint
Abstract: 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 $m>3-\frac{4}{n}$ for $n\in\{2,3\}$ and when $m>1+\frac{n}{4}$ for $n\ge4$. For the fully parabolic system, the same conclusion holds under $m>1+\frac{n}{4}$ for $n\ge4$. 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.
Source: arXiv (Cornell University)
Authors: Bai, Xueli, Li, Fang, Liu, Suying, Luo, Xuxuan
Institutions: Northwestern Polytechnical University, Sun Yat-sen University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1484668164, G2471695747, G8170248098
OpenAlex ID: W7223790314