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arXiv · 2608.05940

Boundary layer analysis for the 2D chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part I: Well-posedness

Hui Wang·Wendong Wang·Lingling Zhao
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Abstract

This is the first part of a two-part work concerning the boundary layer convergence for chemotaxis-Navier-Stokes system in a two-dimensional half-space. In this paper, we investigate the chemotacxis-Navier-Stokes system with the logarithmic singularity under Navier-slip boundary conditions. More precisely, we perform an exact asymptotic expansion for the chemotaxis Navier-Stokes system with viscous coefficient $\varepsilon>0$, and obtain partial boundary layer profiles, establishing the well-posedness of the corresponding boundary layer profiles. Specially, we also establish the local well-posedness of solutions to the supercritical chemotaxis Euler equation (with $\varepsilon=0$) by overcoming the difficulty from the disappearance of diffusion terms.

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Hui Wang, Wendong Wang, Lingling Zhao. 2026-08-06. Boundary layer analysis for the 2D chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part I: Well-posedness. https://arxiv.org/abs/2608.05940

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