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 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics
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Global dynamics of the thermomechanical Cucker-Smale ensemble immersed in incompressible viscous fluids. / Choi, Young Pil; Ha, Seung Yeal; Jung, Jinwook; Kim, Jeongho.
In: Nonlinearity, Vol. 32, No. 5, 12.04.2019, p. 1597-1640.Research output: Contribution to journal › Article
TY - JOUR
T1 - Global dynamics of the thermomechanical Cucker-Smale ensemble immersed in incompressible viscous fluids
AU - Choi, Young Pil
AU - Ha, Seung Yeal
AU - Jung, Jinwook
AU - Kim, Jeongho
PY - 2019/4/12
Y1 - 2019/4/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85067823981&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85067823981&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/aafaae
DO - 10.1088/1361-6544/aafaae
M3 - Article
AN - SCOPUS:85067823981
VL - 32
SP - 1597
EP - 1640
JO - Nonlinearity
JF - Nonlinearity
SN - 0951-7715
IS - 5
ER -