Solvability and blow-up criterion of the thermomechanical Cucker-Smale-Navier-Stokes equations in the whole domain

Jeongho Kim; Weiyuan Zou

doi:10.3934/krm.2020021

Article Contents

2020, Volume 13, Issue 3: 623-651. Doi: 10.3934/krm.2020021

This issue Previous Article The Vlasov-Maxwell-Boltzmann system near Maxwellians with strong background magnetic field Next Article

Solvability and blow-up criterion of the thermomechanical Cucker-Smale-Navier-Stokes equations in the whole domain

Jeongho Kim^1, and
Weiyuan Zou^2, ,

1.
Institute of New Media and Communications, Seoul National University, Seoul 08826, Republic of Korea
2.
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China

^* Corresponding author: Weiyuan Zou
^* Corresponding author: Weiyuan Zou

Received: November 30, 2019

Revised: January 31, 2020

Published: March 2020

The second author Weiyuan Zou is supported by the Fundamental Research Funds for the Central Universities ZY1937

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Abstract

We study local existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker–Smale (in short TCS) model coupled with incompressible Navier–Stokes (NS) equations in the whole space. The coupled system consists of the kinetic TCS equation for particle ensemble and the incompressible NS equations for a fluid via a drag force. For the strong solution, we investigate the blow-up mechanism for the coupled system, and we also study the global existence of a weak solution in the whole space.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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