论文标题
在1-D等粒径Navier-Stokes方程的周期性扰动下大振幅粘性冲击的稳定性
Stability of large-amplitude viscous shock under periodic perturbation for 1-d isentropic Navier-Stokes equations
论文作者
论文摘要
在周期性扰动下，无污染和粘性保护法的解决方案的稳定性是一个有趣而重要的问题。在本文中，考虑了静脉内导航方程的空间周期性扰动下的大振幅粘性冲击。结果表明，如果冲击周围的初始扰动很小，并且满足零质量的条件（2.17），则N-S方程的溶液会以偏移为粘性冲击，这部分由周期性振荡确定。换句话说，即使扰动在远场振荡，粘性冲击是非线性稳定的。关键是要构造合适的ansatz $（\ tilde {v}，\ tilde {u}）$，该$在远场上带有解决方案$（v，u）$的相同振荡，以便差异$（v- \ tilde {v}，v}，u- \ \ tilde tilde $ tilde $ tilde $ tilde $ hef fors $ hh u fors $ h^fors fors fors fors fors fors $ h^2 2 0。$
The stability of solutions under periodic perturbations for both inviscid and viscous conservation laws is an interesting and important problem. In this paper, a large-amplitude viscous shock under space-periodic perturbation for the isentropic Navier-Stokes equations is considered. It is shown that if the initial perturbation around the shock is suitably small and satisfies a zero-mass type condition (2.17), then the solution of the N-S equations tends to the viscous shock with a shift, which is partially determined by the periodic oscillations. In other words, the viscous shock is nonlinearly stable even though the perturbation oscillates at the far fields. The key point is to construct a suitable ansatz $ (\tilde{v},\tilde{u}) $, which carries the same oscillations of the solution $ (v,u) $ at the far fields, so that the difference $ (v-\tilde{v},u-\tilde{u}) $ belongs to the $ H^2(R) $ space for all $ t\geq 0. $
