Short-Time Stability of Scalar Viscous Shocks in the Inviscid Limit by the Relative Entropy Method
Short-Time Stability of Scalar Viscous Shocks in the Inviscid Limit by the Relative Entropy Method
复制标题
用相对熵法研究无粘极限标量粘性激波的短时稳定性
DOI：
10.1137/140961523
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Vasseur
中科院分区：
文献类型：
--
作者：
Kyudong Choi;A. Vasseur
考虑一维空间中具有严格凸通量的粘性标量守恒律的无粘极限。我们证明了对于一类大扰动和对于任何有界时间区间，我们可以在$L^2$中得到尖锐估计。可以选择足够大的扰动来破坏粘性层。这表明对激波的快速收敛并不依赖于粘性层的精细结构。这是由N. Leger [Arch]开发的相对熵方法的首次应用。配给。动力机械。分析的。《科学》，199 (2011),pp. 761—778]和N. Leger和A. Vasseur [Arch。配给。动力机械。分析的。， 201(2011)，第271—302页]对冲击的无粘极限的研究。
We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in $L^2$ for a class of large perturbations and for any bounded time interval. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. This is the first application of the relative entropy method developed by N. Leger [Arch. Ration. Mech. Anal., 199 (2011), pp. 761--778] and N. Leger and A. Vasseur [Arch. Ration. Mech. Anal., 201 (2011), pp. 271--302] to the study of an inviscid limit to a shock.