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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Variations on conservation laws for the wave equation
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by Cathleen Synge Morawetz PDF
Bull. Amer. Math. Soc. 37 (2000), 141-154 Request permission

Abstract:

The first part of this paper, presented as an Emmy Noether lecture in connection with the ICM in Berlin in August 1998, gives some examples of using Noether’s theorem for conservation laws for Tricomi-like equations and for the wave equation. It is also shown that equations which are semilinear variations of the wave equation can very often be handled similarly. The type of estimate obtained can even be used to get otherwise unobtainable local estimates for regularity. The fourth part is an introduction to the relation of black holes to the wave equation mainly showing the results of D. Christodoulou. His results use much more difficult estimates not corresponding at all to those in the first part of the paper.
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Additional Information
  • Cathleen Synge Morawetz
  • Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
  • Email: morawetz@cims.nyu.edu
  • Received by editor(s): July 1, 1999
  • Received by editor(s) in revised form: October 6, 1999
  • Published electronically: January 21, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 37 (2000), 141-154
  • MSC (2000): Primary 35Lxx, 35Mxx, 35Qxx, 83Cxx
  • DOI: https://doi.org/10.1090/S0273-0979-00-00857-0
  • MathSciNet review: 1751947