Local well-posedness for quasi-linear problems: A primer
Local well-posedness for quasi-linear problems: A primer
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DOI：
10.1090/bull/1775
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发表时间：
2020-08
影响因子：
1.3
通讯作者：
M. Ifrim;D. Tataru
中科院分区：
文献类型：
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作者：
M. Ifrim;D. Tataru
证明偏微分方程拟线性问题的局部适定性存在许多困难，其中一些是普遍的，另一些则是更具体的问题。一方面，关于适当的姿态应该意味着什么，一个共同的标准已经存在了很长一段时间，这可以追溯到阿达玛。另一方面，就实现这一目标而言，到目前为止，既有许多变化，也有许多误解。这些说明性笔记的目的是在这个方向上收集一些经典和更新的想法，并将它们组合成一个连贯的路线图，然后可以根据读者的选择问题进行调整。
Proving local well-posedness for quasi-linear problems in partial differential equations presents a number of difficulties, some of which are universal and others of which are more problem specific. On one hand, a common standard for what well-posedness should mean has existed for a long time, going back to Hadamard. On the other hand, in terms of getting there, there are by now both many variations—and also many misconceptions. The aim of these expository notes is to collect a number of both classical and more recent ideas in this direction, and to assemble them into a cohesive roadmap that can be then adapted to the reader’s problem of choice.