Special Session 17: Analysis of chemotaxis models

Global Existence and Asymptotic Behavior for a Swirl-Free 3D Axisymmetric Chemotaxis-Navier-Stokes System
Dongkwang Kim
Ulsan National Institute of Science and Technology (UNIST)
Korea
Co-Author(s):    Kyungkeun Kang, Jaewook Ahn
Abstract:
This talk concerns a three-dimensional chemotaxis-Navier-Stokes system modeling the directed motion of cells toward a consumable chemical substrate. Assuming axisymmetric initial data without swirl, we establish the global existence of unique classical solutions for general tensor-valued sensitivities. The proof relies on coupled a priori estimates to resolve the chemotactic interaction, exploiting the geometric properties of the axisymmetric no-swirl flow. Furthermore, we determine the asymptotic behavior of the global solutions, proving their stabilization to the trivial equilibrium at polynomial decay rates coinciding with those of the linear heat equation.