高维Euler方程组的强松弛极限

利用能量积分, 讨论在初值充分小的情形下, 高维带有阻尼项的Euler方程组光滑解的整体存在性和强松弛极限, 得到了解的一致先验估计, 并证明当松弛时间趋于0时, 整体解的渐近行为由多孔渗流方程控制.

Strong Relaxation Limits of Higher Multidimensional Euler Equations

Using the method of energy integral, we discussed the global existence and strong relaxation limit of smooth solutions for higher dimensional Euler equations with damping when the initial values were sufficiently small, and  obtained the uniform a priori estimates of the solutions. We proved that the asymptotic behavior of the global solution was controlled by the porous media equation when the relaxation time tended to zero.