| Abstract: |
| We study a coupled kinetic-non-Newtonian fluid system on the periodic domain $\mathcal{T}^3$, where particles evolve by a Vlasov equation and interact with an incompressible power-law fluid through a drag force. We prove the global existence of weak solutions for all $p > \frac{8}{5}$, where $p > 1$ denotes the power-law exponent of the fluid`s stress-strain relation. Under an additional uniform boundedness assumption on the particle density, we also establish large-time decay of a modulated energy functional measuring deviation from velocity alignment. The decay rate is algebraic when $p > 2$ and exponential when $\frac{6}{5} \leq p \leq 2$, reflecting the role of fluid dissipation in the large-time dynamics. This is recent joint work with Young-Pil Choi and Jinwook Jung. |
|