merge conflict in conferencia iviscid dissipation

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Germán Correa 2021-08-11 10:22:19 -03:00
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start: 2021-09-16T11:00
end: 2021-09-16T12:30
- titulo: Inviscid dissipation and turbulence
abstract: ''
abstract: 'Turbulence is a phenomenon of wide theoretical and practical interest and an area of research with intense current activity.
Mathematical modeling of turbulence relies, in an essential manner, on a thorough understanding of solutions of the Navier-Stokes
equations at high Reynolds number.
A central question of the mathematical analysis of turbulent flows is whether inviscid dissipation actually occurs and, furthermore,
whether there is dissipation of energy in the vanishing viscosity limit. Smooth solutions of the zero viscosity equations, also known as
the Euler equations, conserve energy over time. However, according to turbulence theory, in turbulent regimes energy should be
dissipated and, additionally, the energy dissipation rate should be non-positive in the vanishing viscosity limit. Clearly, the underlying
flows cannot be smooth.
In 1949 Lars Onsager formulated what is now known as the Onsager Conjecture about the critical regularity which would allow for
inviscid dissipation: solutions of the Euler equations with "more than a 1/3 derivative" (ie Holder continuous with exponent greater than
1/3) should be conservative. In contrast it should be possible to produce solutions with "less than 1/3 derivative" which dissipate energy.
During the last 10 to 12 years this area of research has seen a substantial amount of progress, culminating with the complete settling,
in 2018, of the Onsager Conjecture. Complete? This is the subject of the talk'
pdf: ''
speaker:
nombre: Helena Nussenszveig Lopes