论文标题
关于概率良好的背景下的病理集
Concerning the pathological set in the context of probabilistic well-posedness
论文作者
论文摘要
我们证明了非线性波方程的概率良好的互补结果。更确切地说，我们表明，超批评规律性的Sobolev空间中存在着密集的套装$ s $，因此（与概率的概率良好相反）是由卷积产生的全球平滑解决方案家族，与$ S $的近似认同所产生的$ S $的元素在超级重要的sobole sobolev正常级别不会融合。
We prove a complementary result to the probabilistic well-posedness for the nonlinear wave equation. More precisely, we show that there is a dense set $S$ of the Sobolev space of super-critical regularity such that (in sharp contrast with the probabilistic well-posedness results) the family of global smooth solutions, generated by the convolution with some approximate identity of the elements of $S$, does not converge in the space of super-critical Sobolev regularity.
