Alexander Shnirelman

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Alexander I. Shnirelman ( Russian Александр Шнирельман ; * in Moscow ) is a Russian - Canadian mathematician who deals with partial differential equations.

Shnirelman grew up in Moscow, where his mother taught mathematics at a military school and his father was an astronomer. He received his doctorate in mathematics from Lomonosov University in Moscow in 1972 and then worked in the oil industry of the Soviet Union . University positions were difficult to get for Jews in the Soviet Union at the time. In 1991 he went to Tel Aviv University . He then spent two years at the University of Hull before moving to Concordia University in Montreal in 2004 , where he holds a Canada Research Chair in Applied Mathematics.

In the 1970s he proved theorems about the equal distribution of eigenfunctions for classic ergodic systems (billiards), the subject of so-called quantum ergodicity theorems - the eigenfunctions are the corresponding solutions to the Laplace equation of billiard geometries. This was later continued by Yves Colin de Verdière and Steve Zelditch , among others .

His main area of ​​work are equations of hydrodynamics. Shnirelman obtained important results on the Euler equations of hydrodynamics , which are equations of motion of an incompressible ideal fluid without friction. He proved the ambiguity of the weak solutions of the Euler equations in two dimensions and thus gave further proof of a paradox that Vladimir Scheffer had first found and which was named after both - the existence of turbulent solutions of the Euler equations arising out of nowhere without external forces worked. Its construction (on a two-dimensional torus) was simpler than that of Scheffer. Later the proof of the paradox was further simplified by Scheffer-Shnirelman with new methods ( László Székelyhidi , Camillo De Lellis ).

He also constructed weak solutions of Euler's equations in three dimensions with decreasing energy. He also deals with the mathematical description of the behavior of cartilage and developed a new theory of the degree of mapping of continuous mappings in Banach spaces.

Shnirelman received a Royal Society Research Merit Award .

Web links

Individual evidence

  1. ^ Shnirelman Ergodic properties of Eigenfunctions , Uspekhi Mat. Nauka, 29, 1974, 181-182
  2. ↑ A. Shnirelman On the non-uniqueness of weak solution of the Euler equation , Comm. Pure Appl. Math., 50, 1997, 1261-1286
  3. ↑ Shirelman Weak solutions with decreasing energy of incompressible Euler equations , Comm. Math. Phys., Vol. 210, 2000, pp. 541-603
personal data
SURNAME Shnirelman, Alexander
ALTERNATIVE NAMES Shnirelman, Alexander I .; Шнирельман, Александр (Russian spelling)
BRIEF DESCRIPTION Russian-Canadian mathematician
DATE OF BIRTH 20th century