论文标题
平面Navier-Stokes震撼的时间震荡与空间振荡的冲击
Time-asymptotic stability of planar Navier-Stokes shocks with spatial oscillations
论文作者
论文摘要
本文表明，对于三维可压缩的等粒子纳维尔 - 长方形方程式，平面粘性冲击是时间呈稳定的，可适当地稳定，适合零质量的小初始扰动。特别是，扰动不仅包括$ h^3 $ pert扰动，还包括周期性的振荡，它们在空间无穷大处振荡。在前一种情况下，可以根据初始条件来预测最终的冲击位置，而在后者中，该位置均受到起伏的动力。稳定性分析基于$ l^2 $ - 能量方法。关键点是，由于抗衍生技术的结合以及在正常和横向方向上的使用，可以通过抗衍生技术和庞加莱不平等的使用来消除由于冲击波的压缩而产生的不良影响。
This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the perturbations consist of not only $ H^3 $-perturbations, but also periodic ones that oscillate at spatial infinity. In the former case, the final shock locations can be predicted in terms of the initial conditions, while in the latter the locations are subject to the dynamics of the oscillations. The stability analysis is based on the $L^2$-energy method. The key point is that the bad effect due to the compression of the shock waves can be removed by a combination of an anti-derivative technique and the use of Poincaré inequality in the normal and transversal directions, respectively.
