We propose a coupled system for the interaction between Cucker-Smale
flocking particles and viscous compressible fluids, and present a
global existence theory and time-asymptotic behavior for the
proposed model in the spatial periodic domain $\mathbb{T}^3$. Our model
consists of the kinetic Cucker-Smale model for flocking particles
and the isentropic compressible Navier-Stokes equations for fluids,
and these two models are coupled through a drag force, which is responsible for the asymptotic alignment
between particles and fluid. For the asymptotic flocking behavior,
we explicitly construct a Lyapunov functional measuring the
deviation from the asymptotic flocking states. For a large viscosity
and small initial data, we show that the velocities of Cucker-Smale
particles and fluids are asymptotically aligned to the common
velocity.

https://koasas.kaist.ac.kr/bitstream/10203/278730/1/1078-0947_2014_11_4419.pdf

Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids

Decay estimates for isentropic compressible Navier–Stokes equations in bounded domain

The main aim of this paper is to investigate the large time behavior of the smooth solutions to the three-dimensional isentropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients. For a constant ( > 1), we show the decay rate of the L norm of density.

/pdf/decay-rate-of-the-compressible-navier-stokes-equations-with-jrmkte3dnt.pdf

Decay rate of the compressible Navier-Stokes equations with density-dependent viscosity coefficients

On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance (Mathematical Analysis in Fluid and Gas Dynamics)

孝明田中

Papers

On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance (Mathematical Analysis in Fluid and Gas Dynamics)

孝明 田中

Papers

On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance (Mathematical Analysis in Fluid and Gas Dynamics)

孝明田中