关于Boltzmann方程的空间均匀的ES模型(英文)

On the Spatially Homogeneous ES Model of the Boltzmann Equation

在Prandtl数Pr∈[2/3,∞)的情况下,我们讨论了Boltzmann方程的空间均匀的椭圆统计模型.首先,我们建立了解的存在唯一性.其次,我们证明了该解收敛到平衡态并给出了其Maxwell分布型的下界估计.最后,我们给出了熵等式从而证明了该方程的熵是衰减的.

We discuss the solution properties of the spatially homogeneous ellipsoidal statistical model （ES model） of the Boltzmann equation with Prandtl number Pr E [2/3,∞）. First,we establish the existence and uniqueness result. Second, the trend towards equilibrium and the Maxwellian lower bound estimates of the solution are established. Finally, we prove the entropy identity and obtain dissipation of the entropy of this equation.