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