Publication at Faculty of Mathematics and Physics |
2018
Abstract
We prove the existence of strong solutions to the Cucker-Smale flocking model coupled with an incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for p >= 11/5. The fluid part of the system admits strong solutions while the solutions to the CS part are weak.
The coupling is performed through a drag force on a periodic spatial domain T-3. Additionally, we construct a Lyapunov functional determining the large time behavior of solutions to the system.