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 |
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Pages (from-to) | 1597-1640 |
Number of pages | 44 |
Journal | Nonlinearity |
Volume | 32 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2019 Apr 12 |
Bibliographical note
Publisher Copyright:© 2019 IOP Publishing Ltd & London Mathematical Society.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics