Global solvability and stabilization in a chemotaxis(-Navier)-Stokes system with proliferation (Q6070667)

The author considers a chemotaxis-fluid system with nutrient induced proliferation in bounded domains of \(\mathbb{R}^d\). For \(d=2\) the fluid motion is governed by the Navier-Stokes equations while for \(d=3\) -- by the Stokes equations. Those new source terms make the analysis quite different from the already studied cases. Main results include existence of global-in-time solutions, and their stabilization to homogeneous states as time goes to infinity.