三维空间中带阻尼项的欧拉方程初边值问题的经典解

On Solution of Initial-Boundary Value Problem for 3-Dimensional Euler Equations with Nonlinear Damping

研究了三维空间中带非线性阻尼项的可压缩等熵欧拉方程Dirichlet初边值问题.利用能量估计的方法,在其初边值问题局部解存在的条件下,得到当初值在平衡解附近小扰动时,其经典解整体存在唯一性的结论.

The classical solution for the initial-boundary value problem of the compressible isentropic Euler equations with nonlinear damping in R3 has been investigated in this paper. On condition that the local solution for initial-boundary value problem is existed, and it is obtained that the nonlinear damping does not influence the existence of the solution with perturbation of initial value, and that the classical solution is existed and unique by utilizing energy estimates.