Analysis of Fluids and Related Topics: Magnetohydrodynamic equilibrium in non-axisymmetric toroidal domains: existence of solutions and current singularities, Antoine Cerfon, New York University

Analysis of Fluids and Related Topics
  • Antoine Cerfon
  • New York University
  • Magnetohydrodynamic equilibrium in non-axisymmetric toroidal domains: existence of solutions and current singularities
Feb 20, 2020
4:30 pm
Fine Hall 322

Speaker: Antoine Cerfon

Abstract:  The construction of magnetohydrodynamic equilibria in non-axisymmetric toroidal domains is a notoriously challenging problem. The existence of solutions for smooth pressure profiles has not been proved, and empirical results suggest that non-integrable singularities for the current density are generically obtained for such pressure profiles. In this presentation, I will describe the mathematical nature of the difficulties, discuss the special cases in which proofs of existence do exist, and present preliminary theoretical and numerical results which suggest a promising direction for a proof of existence and the numerical construction of equilibria in a robust manner.