Philip Isett

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Philip J. Isett (* 1986 ) is an American mathematician who studies partial differential equations (PDE), in particular regularity problems in PDE in hydrodynamics.

Isett graduated from the University of Maryland at College Park with a Bachelor of Arts and Bachelor of Science in 2008. He received his PhD in 2013 with Sergiu Klainerman at Princeton University . As a post-doctoral student he was a Moore Instructor at the Massachusetts Institute of Technology and a Post-Doctoral Scholar at the National Science Foundation . He was Assistant Professor at the University of Texas at Austin from 2016 and Professor at Caltech from 2018 .

He succeeded in completely solving the Onsager problem in 2017 ( Lars Onsager 1949). It is about a limit of one third for the exponent of the Hölder continuity in weak solutions of the three-dimensional incompressible Euler equation of hydrodynamics. Below the bound, he found weak solutions with a violation of energy conservation (so-called anomalous dissipation), which Onsager already suspected (who generally assumed that the Euler equation - although the limit case of the Navier-Stokes equation without internal friction (viscosity) - shows phenomena similar to turbulence, such as abnormal dissipation and large fluctuations in speed). Energy conservation had previously been proven above the limit. Isett used methods of convex integration, which Camillo De Lellis and László Székelyhidi had introduced when investigating the Euler equation. Important preliminary work also came from Tristan Buckmaster and Vlad Vicol , among others . Isett also investigated what exactly happens locally in the anomalous dissipation of the Euler equations.

In 2017 he proved that Hölder-continuous globally dissipative weak solutions of the incompressible three-dimensional Euler equations (i.e. with the validity of the energy inequality) can be ambiguous and violate the conservation of energy (the kinetic energy is considered) (anomalous dissipation). These pathological solutions can even have positive Hausdorff measures in the energy space under fixed initial conditions, and the initial conditions at which this behavior occurs are close. For the proof he used a new method of convex integration.

In 2019 he received the Clay Research Award with Tristan Buckmaster and Vlad Vicol (who also did important preliminary work in solving the Onsager conjecture). In 2019 he received a Sloan Research Fellowship.

Fonts (selection)

  • with Tristan Buckmaster, Camillo De Lellis, Laszlo Székelyhidi: Anomalous dissipation for 1/5-Hölder Euler flows, Annals of Mathematics, Volume 182, 2015, pp. 127–172
  • A proof of Onsager's conjecture, Annals of Mathematics, Volume 188, 2018, pp. 871-963, Arxiv
  • Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time, Annals of Mathematical Studies, Princeton UP 2017, Arxiv Preprint
  • Nonuniqueness and existence of continuous, globally dissipative Euler flows, Arxiv 2017

Web links

Individual evidence

  1. ↑ Philip Isett in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Isett, A proof of Onsager's conjecture, Annals of Mathematics, Volume 188, 2018, pp. 871-963
  3. ↑ Peter Constantin , Weinan E , Edriss S. Titi, Onsager's conjecture on the energy conservation for solutions of Euler's equation, Comm. Math. Phys., Vol. 165, 1994, pp. 207-209
  4. ^ Clay Research Award 2019
  5. ↑ Caltech Mathematics Professor Wins 2019 Sloan Fellowship , Caltech February 19, 2019
personal data
SURNAME Isett, Philip
ALTERNATIVE NAMES Isett, Philip J.
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH 1986