一般无界区域中带有阻尼的三维可压缩欧拉方程

The 3D Compressible Euler Equations with Damping in the General Unbounded Domain

考虑在一般的三维无界区域中的具有滑移边界条件的带有阻尼的可压缩欧拉方程.当初始值接近平衡态时,获得了全局存在性和唯一性.同时,研究了在半空间情形下系统的衰减率.证明了经典解的L^2范数以(1+t)-3/4衰减到常值背景解.

In this paper,the authors consider the 3D damped compressible Euler equations in the general unbounded domain with slip boundary condition.The authors obtain the global existence and uniqueness when the initial data is near its equilibrium.Meanwhile,they also investigate the decay rates of the system in the half space.The authors show that the classical solution decays in the L^2-norm to the constant background state at the rate of (1+t)-(3/4).