LOCAL WELL-POSEDNESS FOR QUASI-LINEAR PROBLEMS: A PRIMER

被引：13

作者：

Ifrim, Mihaela ^{[1
]}

Tataru, Daniel ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53705 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA USA

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 60卷 / 02期

关键词：

CAUCHY-PROBLEM; SCHRODINGER-EQUATIONS; CALCULUS;

D O I：

10.1090/bull/1775

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：167 / 194

页数：28

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