Chemotaxis(-fluid) systems with logarithmic sensitivity and slow consumption: global generalized solutions and eventual smoothness
Mario Fuest
TL;DR
This paper studies a chemotaxis-fluid system with logarithmic sensitivity and slow nutrient consumption, establishing the existence of global generalized solutions and their eventual smoothness under certain conditions.
Contribution
It introduces a novel analysis of chemotaxis-fluid models with logarithmic sensitivity, proving global solutions and smoothness over time.
Findings
Existence of global generalized solutions
Solutions become smooth after some time
The model handles slow nutrient consumption effectively
Abstract
We consider the system \begin{align*} \begin{cases} n_t + u \cdot \nabla n = \Delta n - \chi \nabla \cdot (\frac{n}{c} \nabla c),
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Taxonomy
TopicsMathematical Biology Tumor Growth · Advanced Mathematical Modeling in Engineering · Cellular Mechanics and Interactions