A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data

Seung-Yeal Ha; Bingkang Huang; Qinghua Xiao; Xiongtao Zhang

doi:10.3934/cpaa.2020039

Article Contents

2020, Volume 19, Issue 2: 835-882. Doi: 10.3934/cpaa.2020039

This issue Previous Article Pathwise solution to rough stochastic lattice dynamical system driven by fractional noise Next Article Dynamics in a diffusive predator-prey system with stage structure and strong allee effect

A global existence of classical solutions to the two-dimensional kinetic-fluid model for flocking with large initial data

1.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
2.
Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Republic of Korea
3.
School of Mathematics, Hefei University of Technology, Hefei 230009, China
4.
Wuhan Institute of Physics and Mathematicss, Chinese Academy of Science, Wuhan 430071, China
5.
Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China

^* Corresponding author
^* Corresponding author

Received: November 30, 2018

Revised: May 31, 2019

Published: October 2019

The work of S.-Y. Ha is supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03, the work of Qinghua Xiao was supported by grants from Youth Innovation Promotion Association and the National Natural Science Foundation of China #11871469, #11501556, and the work of Xiongtao Zhang was supported by grant the National Natural Science Foundation of China #11801194

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Abstract

We present a two-dimensional coupled system for flocking particle-compressible fluid interactions, and study its global solvability for the proposed coupled system. For particle and fluid dynamics, we employ the kinetic Cucker-Smale-Fokker-Planck (CS-FP) model for flocking particle part, and the isentropic compressible Navier-Stokes (N-S) equations for the fluid part, respectively, and these separate systems are coupled through the drag force. For the global solvability of the coupled system, we present a sufficient framework for the global existence of classical solutions with large initial data which can contain vacuum using the weighted energy method. We extend an earlier global solvability result [20] in the one-dimensional setting to the two-dimensional setting.

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Mathematics Subject Classification: Primary: 35A01, 35K45; Secondary: 76N10.

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