Pré-Publication, Document De Travail Année : 2025

Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains

Solutions fortes du système de Keller-Segel-Navier-Stokes dans des domaines lipschitziens bornés

Résumé

Consider the coupled Keller-Segel-Navier-Stokes or the chemotaxis-consumption- Navier-Stokes system in bounded Lipschitz domains for general coupling terms which, e.g., include buoyancy forces. It is shown that these systems admit 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 presented is based on optimal Lq -regularity properties of the Neumann Laplacian and the Stokes operator in bounded Lipschitz domains.

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Dates et versions

hal-05060200 , version 1 (08-05-2025)

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  • HAL Id : hal-05060200 , version 1

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Matthias Hieber, Hideo Kozono, Sylvie Monniaux, Patrick Tolksdorf. Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains. 2025. ⟨hal-05060200⟩
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