Global well-posedness for the two-dimensional coupled chemotaxis-generalized Navier-Stokes system with logistic growth (Q2184717)

A chemotaxis-fluid system is considered in the whole plane. The Keller-Segel part of that model features a logistic reaction term, and the Navier-Stokes part has a modified diffusion term described by the fractional power of the Laplacian \(-(-\Delta)^\alpha\). The authors study well-posedness of the Cauchy problem for \(\alpha\in[\frac12,1]\), establish global in time solvability and some regularity of the solutions. A subtle estimate on the associated vorticity function in \(L^{\frac43}({\mathbb R}^2)\) is derived.