Vladimir Scheffer

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Vladimir Scheffer (born November 8, 1950 ) is an American mathematician who deals with partial differential equations and geometric measure theory.

Scheffer received his doctorate in 1974 under Frederick Almgren at Princeton University ( Regularity and Irregularity of Solutions to Nonlinear Second-Order Elliptic Systems of Partial Differential Equations and Inequalities ). He was a professor at Rutgers University and is a professor at Princeton University.

In 1993 he proved the existence of paradoxical weak solutions of the Euler equations of ideal incompressible liquids, which correspond to the sudden occurrence of turbulent flows without external stimulation (Scheffer-Shnirelman paradox according to Scheffer and Alexander Shnirelman ). The proof was complicated (even in Shnirelman's simplification a few years later), and in 2008 László Székelyhidi and Camillo De Lellis gave a simpler proof using new methods.

He also contributed to the Caffarelli - Kohn - Nirenberg theorem about partial regularity (or the character of singularities) of the solutions of the three-dimensional Navier-Stokes equation .

In 2000 he published with Jean Taylor an extensive postponed proof of his teacher Almgren from the geometric measurement theory ( regularity theorem of Almgren ). He translated the book on Ergodic Theory by Jakow Grigorjewitsch Sinai from Russian (Ergodic Theory, Princeton University Press 1976).

In 1981 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ). In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( A self-focusing solution of the Navier-Stokes equations with a speed-reducing external force ).

Fonts (selection)

Except for the works cited in the footnotes.

  • A solution to the Navier-Stokes inequality with an internal singularity, Comm. Math. Phys., Vol. 101, 1985, pp. 47-85
  • The Navier-Stokes equations on a bounded domain, Comm. Math. Phys., Vol. 73, 1980, pp. 1-42
  • Boundary regularity for the Navier-Stokes equations in half-space, Comm. Math. Phys., Vol. 85, 1982, pp. 275-299
  • Estimates on the vorticity of solutions to the Navier-Stokes equations, Comm. Math. Phys., Vol. 81, 1981, pp. 379-400
  • Nearly one dimensional singularities of solutions to the Navier-Stokes inequality, Comm. Math. Phys., Vol. 110, 1987, pp. 525-551
  • The Navier-Stokes equations in space dimension four, Comm. Math. Phys., Vol. 61, 1978, pp. 41-68
  • Hausdorff measure and the Navier-Stokes equations, Comm. Math. Phys., Vol. 55, 1977, pp. 97-112
  • Turbulence and Hausdorff dimension, in: Turbulence and the Navier-Stokes equations, Lecture Notes in Mathematics 565, Springer Verlag, 1976, pp. 94-112
  • Partial regularity solutions to the Navier Stokes equations, Pacific J. Math., Vol. 66, 1976, pp. 535-552

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Vladimir Scheffer On inviscid flow with compact support in space-time , J. Geom. Anal. 3, 1993, 343-401
  3. ↑ A. Shnirelman On the non-uniqueness of weak solution of the Euler equation , Comm. Pure Appl. Math., 50, 1997, 1261-1286
  4. ↑ Cédric Villani Paradoxe de Scheffer-Shnirelman revu sous l'angle de l'integration convexe, d'après C. De Lellis et L. Szekelyhidi , Seminaire Bourbaki, No. 1001, November 2008
personal data
SURNAME Scheffer, Vladimir
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH November 8, 1950