We provide a lower bound for the blow up time of the $H^2$ norm of the entropy solutions of the inviscid Burgers equation in terms of the $H^2$ norm of the initial datum. This shows an interesting symmetry of the Burgers equation: the invariance of the space $H^2$ under the action of such nonlinear equation. The argument is based on a priori estimates of energy and stability type for the (viscous) Burgers equation.

中文翻译：

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无粘性Burgers方程中的奇点形成

我们为 $H^{\mathrm{2个}}$ 关于无粘性Burgers方程的熵解的范数 $H^{\mathrm{2个}}$初始基准的范数。这显示了Burgers方程有趣的对称性：空间的不变性$H^{\mathrm{2个}}$在这种非线性方程的作用下。该论点基于（粘稠）Burgers方程的能量和稳定性类型的先验估计。