ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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           ELTE TTK Fizikai Intézet
       STATISZTIKUS FIZIKAI SZEMINÁRIUM


             2019. december 4.

                   szerda 

                   11.00

               Norbert Barankai

  MTA-ELTE Theoretical Physics Research Group

   "Onsager's ideal turbulence: results in 2D"


In 1949, Lars Onsager wrote the article entitled
´Statistical hydrodynamics´  which appeared in 
Nouvo Cimento. This is the only published work of
Onsager in the field of turbulence. However, his 
insights led him to groundbreaking contributions
to turbulence theory in two and three spatial 
dimensions. In two dimensions, Onsager performed
a Gibbsian analysis of the Helmholtz-Kirchoff
model and discovered  negative temperature states,
which preceded the discovery of the same phenomena
by Purcell and Pound in nuclear-spin systems in 
1951. The qualitative results of the statistical 
analysis were able to explain the prevalence of 
large, steady vortices observed in two dimensional
flows of high Reynolds number. In three dimensions,
Onsager formulated a conjecture concerning regularity
of incompressible solutions of Euler equations and 
the anomalous dissipation observed in ideal turbulent
flows. 

In these two seminars, we review the mathematical 
development of Onsager's ideas which culminated in
the proof of Onsager's conjecture in 2017: weak 
solutions of the Euler equation of which Hölder 
exponent is greater than 1/3 always conserve energy
but there are dissipative weak solutions with Hölder
exponent less than 1/3. The proof involved the work
of several mathematicians in the last decade of whom
we mention László Székelyhidi Jr, Camillo de Lellis 
and Philip Isett.     





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        honlap: http://glu.elte.hu/~statfiz

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