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Navier–Stokes Hierarchies of Reduced MHD Models in Tokamak Geometry

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Abstract

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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Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06 UMR 7598 Laboratoire Jacques-Louis Lions, 75005, Paris, France

    Bruno Després

  2. Léonard de Vinci Pole Universitaire De Vinci Research Center (DVRC), 92916, Paris La Défense, France

    Rémy Sart

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  1. Bruno Després
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Correspondence to Bruno Després.

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Communicated by E. Feireisl

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Després, B., Sart, R. Navier–Stokes Hierarchies of Reduced MHD Models in Tokamak Geometry. J. Math. Fluid Mech. 20, 329–357 (2018). https://doi.org/10.1007/s00021-017-0323-8

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