We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.
Bibliographical noteFunding Information:
Yun-Sung Chung's work is supported by No. NRF-2012R1A1A2001373 and Kyungkeun Kang's work is supported by No. NRF-2014R1A2A1A11051161 and NRF20151009350.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics