| Abstract: |
| We study the coupled Keller-Segel-Navier-Stokes system in bounded Lipschitz domains. It is shown that the system admits local strong as well as global strong solutions for small data in the setting of critical Besov spaces. Moreover, non-trivial equilibria are shown to be exponentially stable. For smoother data, these solutions are shown to be globally bounded and to preserve positivity properties.
The approach is based on optimal $L^q$-regularity properties of the Neumann Laplacian and the Stokes operator on bounded Lipschitz domains. |
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