Large time periodic solutions to coupled chemotaxis-fluid models

Abstract

In this paper, we deal with the time periodic problem to coupled chemotaxis-fluid models. We prove the existence of large time periodic strong solutions for the full chemotaxis-Navier–Stokes system in spatial dimension \(N=2\), and the existence of large time periodic strong solutions for the chemotaxis-Stokes system in spatial dimension \(N=3\). On the basis of these, the regularity of the solutions can be further improved. More precisely speaking, if the time periodic source g and the potential force \(\nabla \varphi \) belong to \(C^{\alpha , \frac{\alpha }{2}}(\overline{\Omega }\times \mathbb R)\), the solutions we obtained are also classical solutions.