论文标题
亚音线周期溶液的全球存在和稳定性在有界域中阻尼可压缩的Euler方程
Global existence and stability of subsonic time-periodic solution to the damped compressible Euler equations in a bounded domain
论文作者
论文摘要
在本文中，我们考虑具有源任期$β（t，x）ρ| u |^αu$的一维等速压缩欧拉方程在一个有界域中，可以用来描述喷嘴中的气体传输。解决方案在初始和边界数据的小扰动下是稳定的。然后可以将相应的线性化系统解耦。〜唯一性是稳定性的直接副产品。阻尼系数没有小假设。
In this paper, we consider the one-dimensional isentropic compressible Euler equations with source term $β(t,x)ρ|u|^αu$ in a bounded domain, which can be used to describe gas transmission in a nozzle.~The model is imposed a subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger an unique subsonic time-periodic smooth solution and this unique periodic solution is stable under small perturbations on initial and boundary data.~To get the existence of subsonic time-periodic solution, we use the linear iterative skill and transfer the boundary value problem into two initial value ones by using the hyperbolic property of the system. Then the corresponding linearized system can be decoupled.~The uniqueness is a direct by-product of the stability. There is no small assumptions on the damping coefficient.
