Some Open Problems and Research Directions in the Mathematical Study of Fluid Dynamics

Peter Constantin

A chapter in Mathematics Unlimited — 2001 and Beyond, 2001, pp 353-360 from Springer

Abstract: Abstract In an editorial of the Notices of the AMS (vol. 47, Number 3, March 2000), Felix Browder, President of the AMS, refers to “ ... some of the major classical problems: the Riemann Hypothesis, the Poincaré Conjecture, and the regularity of three-dimensional fluid flows”. I imagine that many beginning graduate students in Mathematics have heard of the first two of these problems, but maybe not so many know about the third. I would like to describe here this third problem in a broader context, involving not only PDE questions of existence, uniqueness and regularity of solutions, but also dynamical issues concerning stability and statistical questions raised by instability.

Date: 2001
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DOI: 10.1007/978-3-642-56478-9_15

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