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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:László Székelyhidi\, IAS and Leipzig\n\nAbstract: The ideal MHD
system in three space dimensions consists of the incompressible Euler equa
tions coupled to the Faraday system via Ohm's law. This system has a wealth
of interesting structure\, including three conserved quantities: the total
energy\, cross-helicity and magnetic helicity. Whilst the former two are a
nalogous (and analytically comparable) to the total kinetic energy for the
Euler system\, magnetic helicity is known to be more robust and of a differ
ent nature. In particular\, when studying weak solutions\, Onsager-type con
ditions for all three quantities are known\, and are basically on the same
level of 1/3-differentiability as the kinetic energy in the ideal hydrodyna
mic case for the former two. In contrast\, magnetic helicity does not requi
re any differentiability\, only L^3 integrability. From the physical point
of view this difference lies at the heart of the Taylor-Woltjer relaxation
theory. From the mathematical point of view it turns out to be closely rela
ted to the div-curl structure of the Faraday system. In the talk we present
and compare some recent constructions of weak solutions and\, along the wa
y highlight some of the hidden structures in the ideal MHD system. Joint wo
rk with Daniel Faraco and Sauli Lindberg.
DTEND:20220425T233000Z
DTSTAMP:20240412T221445Z
DTSTART:20220425T223000Z
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SEQUENCE:0
SUMMARY:CAMS Colloquium: Magnetohydrodynamic Turbulence: weak solutions and
conserved quantities
UID:tag:localist.com\,2008:EventInstance_39608742491179
URL:https://calendar.usc.edu/event/cams_colloquium_magnetohydrodynamic_turb
ulence_weak_solutions_and_conserved_quantities
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