Magnetohydrodynamic Turbulence - Weak Solutions and Conserved Quantities

Explore the complexities of magnetohydrodynamic turbulence in this 58-minute seminar presented by László Székelyhidi from the University of Leipzig. Delve into the ideal magnetohydrodynamic system in three space dimensions, examining its structure and three conserved quantities: total energy, cross-helicity, and magnetic helicity. Compare the analytical properties of these quantities to the total kinetic energy in the Euler system, with a focus on the unique robustness of magnetic helicity. Investigate Onsager-type conditions for weak solutions and their implications for differentiability requirements. Discover the connection between the physical Taylor-Woltjer relaxation theory and the mathematical div-curl structure of the Faraday system. Gain insights into recent constructions of weak solutions and uncover hidden structures within the ideal magnetohydrodynamic system through this joint work with Daniel Faraco and Sauli Lindberg.