Eventual smoothness in a chemotaxis-Navier-Stokes system with indirect signal production involving Dirichlet signal boundary condition (Q6613005)

This article treats a chemotaxis system featuring logistic-type source terms (\(+rn-\mu n^{\alpha}\)) and indirect consumption of the signal (which may enter the system via possibly non-zero Dirichlet boundary conditions), coupled to a Navier-Stokes fluid. In 3-dimensional bounded domains \(\Omega\), global existence of weak solutions is proven under the condition that \(\alpha>\frac 43\). Additionally, if \(r\) is small compared to \(\mu\), this solution is smooth on \(\Omega\times(T,\infty)\) for some \(T>0\).