Abstract
We study a global dynamics of the thermomechanical Cucker-Smale (TCS) particles immersed in incompressible viscous fluid. For this, we use a coupled system consisting of kinetic TCS equation for particles and incompressible Navier-Stokes for fluid via a drag force in three dimensions. We first show the global existence of weak solutions for large data, and then establish the global existence and uniqueness of strong solutions under a smallness assumption on the initial data. We also provide a priori estimate of large-time behavior of strong solutions which exhibits an exponential alignment between TCS particles and fluid asymptotically.
| Original language | English |
|---|---|
| Pages (from-to) | 1597-1640 |
| Number of pages | 44 |
| Journal | Nonlinearity |
| Volume | 32 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2019 Apr 12 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics
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Choi, Y. P., Ha, S. Y., Jung, J., & Kim, J. (2019). Global dynamics of the thermomechanical Cucker-Smale ensemble immersed in incompressible viscous fluids. Nonlinearity, 32(5), 1597-1640. https://doi.org/10.1088/1361-6544/aafaae