We discuss recent progress in the understanding of the global behavior of solutions to critical non-linear dispersive equations. The emphasis is on global existence, scattering and finite time blow-up. For solutions that are bounded in the critical norm, but which blow-up in finite time, we also discuss the issue of universal profiles at the blow-up time.

中文翻译：

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关键的非线性色散方程：整体存在，散射，爆炸和通用分布

我们讨论了对临界非线性色散方程解的整体行为的理解的最新进展。重点是全局性存在，分散和有限时间爆炸。对于受关键规范约束但在有限时间内爆炸的解决方案，我们还讨论了爆炸时的通用轮廓问题。