波尔兹曼方程到欧拉方程黎曼解的流体动力学极限

The hydrodynamic limit toward the Riemann solutions of the compressible Euler equation from the Boltzmann equation

文章回顾了Huang等关于波尔兹曼方程到欧拉方程一般黎曼解的流体动力学极限.黎曼解由激波、稀疏波和接触间断波的任意线性组合复合而成.通过引进两类双曲波并结合尺度变换及精细的能量估计方法,成功证明了以上流体动力学极限并得到了收敛速率.

In this survey paper,we shall recall Huang’s works on the hydrodynamic limit from the Boltzmann equation to the compressible Euler equation in the setting of Riemann solutions.The Riemann solutions consist of shock,rarefaction and contact discontinuity.Through introducing two kinds of hyperbolic waves and applying scaling method and elaborate energy estimates,we successfully justify the above limit.Moreover the convergence rate is also obtained.