Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 2, pp 329–357 | Cite as

Navier–Stokes Hierarchies of Reduced MHD Models in Tokamak Geometry



We study the closure of reduced MHD models, such as the ones which are used in the modeling of Tokamaks and ITER, see Franck et al. (ESAIM: M2AN 49(5), 2015) and Guillard (2015) and references therein. We show how to modify the entropy moment methods to obtain a hierarchy of Navier–Stokes like models in potential formulation with a correct energy balance. Our procedure is well adapted to the complicated geometry of the torus. We obtain mainly two original results. One is a comparison principle between all these models: it explains that the dynamics of a reduced model is a lower bound of the dynamics of the initial model. The other one the existence of a weak solution to some of these complicate models adapted to the Tokamak geometry.


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© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Sorbonne Universités, UPMC Univ Paris 06 UMR 7598 Laboratoire Jacques-Louis LionsParisFrance
  2. 2.Léonard de Vinci Pole Universitaire De Vinci Research Center (DVRC)Paris La DéfenseFrance

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