We show the vanishing viscosity limit to entropy shocks for the fractal Burgers equation in one space dimension. More precisely, we quantify the rate of convergence of the inviscid limit in $L^2$ for large initial perturbations around the entropy shock on any bounded time interval. This is the first result on the inviscid limit to entropy shock for the fractal Burgers equation with the quantified convergence, for large initial perturbations.

中文翻译：

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分形伯格斯方程冲击波的无粘性极限

我们展示了在一维空间中分形伯格斯方程的熵冲击的消失粘度极限。更准确地说，我们量化了在任何有界时间间隔内熵冲击周围的大初始扰动的无粘性极限的收敛速度，以 $L^2$ 表示。对于大的初始扰动，这是具有量化收敛的分形 Burgers 方程熵冲击无粘性极限的第一个结果。