论文标题
在周期性扰动下，粘性接触波和两个稀疏波的组合的渐近稳定性
Asymptotic stability of the combination of a viscous contact wave with two rarefaction waves for 1-D Navier-Stokes equations under periodic perturbations
论文作者
论文摘要
考虑到空间周期性扰动，我们证明了本文中粘性接触波的复合波和两个稀疏波的复合波的时间 - 呈现稳定性。这种扰动在远处不断振荡，无法整合。关键是要构建一个携带相同振荡％的合适的ANSATZ，消除了溶液的振荡，与\ cite {Huangxuyuan2020，Huangyuan2021}中的振荡，但由于接触不连续性的退化，构造的结构更加微妙。我们找到了一种将相同重量函数用于不同变量和波浪模式的方法，这仍然确保错误可控。因此，该结构可用于接触不连续性和复合波。最后，通过能量法，我们证明了库奇问题在空间周期性扰动下承认了独特的全球时间解决方案，复合波仍然稳定。
Considering the space-periodic perturbations, we prove the time-asymptotic stability of the composite wave of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations in this paper. This kind of perturbations keep oscillating at the far field and are not integrable. The key is to construct a suitable ansatz carrying the same oscillation %eliminating the oscillation of the solution as in \cite{HuangXuYuan2020,HuangYuan2021}, but due to the degeneration of contact discontinuity, the construction is more subtle. We find a way to use the same weight function for different variables and wave patterns, which still ensure the errors be controllable. Thus, this construction can be applied to contact discontinuity and composite waves. Finally, by the energy method, we prove that the Cauchy problem admits a unique global-in-time solution and the composite wave is still stable under the space-periodic perturbations.
