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  • From: StatFizSzeminar <statfiz AT>
  • To: fizinfo AT
  • Subject: [Fizinfo] Stat Fiz Szeminarium
  • Date: Sun, 01 Dec 2019 11:02:57 +0100

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ELTE TTK Fizikai Intézet

2019. december 4.



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

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.

1117, Budapest, Pázmány P. sétány 1/A, Északi tömb 2.54

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