论文标题
平滑不会为具有有限自主域的传输方程提供选择原理
Smoothing does not give a selection principle for transport equations with bounded autonomous fields
论文作者
论文摘要
我们在$ \ mathbb r^3 $中举例说明了一个有界差异的自主矢量字段（以及$ \ mathbb r^2 $中的非自主有限差异的免费矢量字段，以及对相应传输方程的Cauchy问题的有界初始数据。然后，我们表明，这两个解决方案都是传输方程的经典解的限制，用于适当的向量场和初始数据的平滑。
We give an example of a bounded divergence free autonomous vector field in $\mathbb R^3$ (and of a nonautonomous bounded divergence free vector field in $\mathbb R^2$) and of a bounded initial data for which the Cauchy problem for the corresponding transport equation has $2$ distinct solutions. We then show that both solutions are limits of classical solutions of transport equations for appropriate smoothings of the vector fields and of the initial data.
