Local well-posedness for quasi-linear problems: A primer
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- by Mihaela Ifrim and Daniel Tataru HTML | PDF
- Bull. Amer. Math. Soc. 60 (2023), 167-194 Request permission
Abstract:
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.
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Additional Information
- Mihaela Ifrim
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Madison, Wisconsin
- MR Author ID: 995443
- ORCID: 0000-0002-0491-5174
- Email: ifrim@wisc.edu
- Daniel Tataru
- Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California
- MR Author ID: 267163
- ORCID: 0000-0001-9654-152X
- Email: tataru@math.berkeley.edu
- Received by editor(s): February 23, 2022
- Published electronically: July 27, 2022
- Additional Notes: The first author was supported by a Luce Professorship, by the Sloan Foundation, and by an NSF CAREER grant DMS-1845037.
The second author was supported by the NSF grant DMS-1800294 as well as by a Simons Investigator grant from the Simons Foundation. - © Copyright 2022 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 60 (2023), 167-194
- MSC (2020): Primary 35L45, 35L50, 35L60
- DOI: https://doi.org/10.1090/bull/1775