CONVEX INTEGRATION CONSTRUCTIONS IN HYDRODYNAMICS

TRISTAN BUCKMASTER, VLAD VICOL

Research output: Contribution to journalArticlepeer-review

Abstract

We review recent developments in the field of mathematical fluid dynamics which utilize techniques that go under the umbrella name convex integration. In the hydrodynamical context, these methods produce paradoxical solutions to the fluid equations which defy physical laws. These counterintuitive solutions have a number of properties that resemble predictions made by phenomenological theories of fluid turbulence. The goal of this review is to highlight some of these similarities while maintaining an emphasis on rigorous mathematical statements. We focus our attention on the construction of weak solutions for the incompressible Euler, Navier–Stokes, and magneto-hydrodynamic equations which violate these systems’ physical energy laws.

Original languageEnglish (US)
Pages (from-to)1-44
Number of pages44
JournalBulletin of the American Mathematical Society
Volume58
Issue number1
DOIs
StatePublished - 2021

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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