Zero-viscosity limit of the chemotaxis-Navier-Stokes equations with the Navier-slip boundary condition
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911643305246720 |
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| author | Li, Bolun Shi, Fengqiang Wang, Wendong |
| author_facet | Li, Bolun Shi, Fengqiang Wang, Wendong |
| contents | The interplay of chemotaxis and diffusion of nutrients or signaling chemicals in bacterial suspensions can produce a variety of structures with locally high concentrations of cells, including phyllotactic patterns, filaments, and concentrations in fabricated microstructures, which is described by the chemotaxis-Navier-Stokes flow by Tuval et al. in 2005. Dombrowski et al. also observed that Bacterial flow in a sessile drop related to those in the Boycott effect of sedimentation can carry bioconvective plumes, viewed from below through the bottom of a petri dish, and the horizontal "turbulence" white line near the top is the air-water-plastic contact line. It's interesting to verify these turbulent phenomena mathematically. For varying chemotactic and velocity viscosities, we derive the boundary layer equations of the chemotaxis-Navier-Stokes system rigorously in a two-dimensional half-space under the Navier-slip boundary condition and obtain the vanishing viscosity limit of the 2D chemotaxis-fluid coupled system in the anisotropic conormal Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02394 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero-viscosity limit of the chemotaxis-Navier-Stokes equations with the Navier-slip boundary condition Li, Bolun Shi, Fengqiang Wang, Wendong Analysis of PDEs The interplay of chemotaxis and diffusion of nutrients or signaling chemicals in bacterial suspensions can produce a variety of structures with locally high concentrations of cells, including phyllotactic patterns, filaments, and concentrations in fabricated microstructures, which is described by the chemotaxis-Navier-Stokes flow by Tuval et al. in 2005. Dombrowski et al. also observed that Bacterial flow in a sessile drop related to those in the Boycott effect of sedimentation can carry bioconvective plumes, viewed from below through the bottom of a petri dish, and the horizontal "turbulence" white line near the top is the air-water-plastic contact line. It's interesting to verify these turbulent phenomena mathematically. For varying chemotactic and velocity viscosities, we derive the boundary layer equations of the chemotaxis-Navier-Stokes system rigorously in a two-dimensional half-space under the Navier-slip boundary condition and obtain the vanishing viscosity limit of the 2D chemotaxis-fluid coupled system in the anisotropic conormal Sobolev spaces. |
| title | Zero-viscosity limit of the chemotaxis-Navier-Stokes equations with the Navier-slip boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.02394 |