二维线性化Navier-Stokes-Poisson方程解的逐点估计

POINTWISE ESTIMATE OF SOLUTION TO LINEARIZED NAVIER-STOKES-POISSON SYSTEM IN TWO SPACE DIMENSION

本文研究了二维空间线性化的等熵可压缩Navier-Stokes-Poisson方程柯西问题.通过把方程组转变成关于单个函数的方程,求解出各个函数,得到方程组的格林函数.利用对格林函数的详细分析,获得了方程组解的逐点估计.结果显示方程组中电流密度以热核的速度衰减,动量密度衰减慢得多,且其L2范数不衰减.

Cauchy problem of linearized Navier-Stokes-Poisson system in two dimensional space is considered.Through changing the system into several equations for single function,we solved the function and got the Green function for the system.Using detailed analysis of the Green function,we got pointwise estimation of the solution.The result shows electron°uid density decays as fast as heat kernel,but momentum decays slower,even though its L2 norm does not decay.