三维不可压缩非牛顿流体/Vlasov方程组的大时间行为

Large-time behavior of three-dimensional incompressible non-Newtonian fluid/Vlasov equations

主要考虑三维周期空间中流体与粒子方程组的大时间行为,准确地说,该模型由不可压缩非牛顿流体方程及Vlasov方程通过阻力项耦合而成.对于此模型,利用Lyapunov函数估计其时间衰减率,得到粒子与流体弱解的能量随着时间的推移呈指数衰减.

In this paper,we consider the large-time behavior for the coupled kinetic-fluid equations in the three-dimensional periodic spatial domain.More precisely,we consider the incompressible nonNewtonian fluid coupled to Vlasov equations through a drag forcing term.For this system,we employ a Lyapunov functional to estimate its time decay rate.The exponential alignment between particles and fluid velocities as time evolves is obtained.