# Well-posedness for chemotaxis-fluid models in arbitrary dimensions

@inproceedings{Diebou2021WellposednessFC, title={Well-posedness for chemotaxis-fluid models in arbitrary dimensions}, author={Gael Yomgne Diebou}, year={2021} }

. We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity preservation are constructed for low regularity data in 2 and higher dimensions under suitable conditions. Our initial data classes involve a new scale of function space, that is L − 1 2 ,N − 2 ( R N ) which collects divergence of vector-ﬁelds with components in…

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