Methods and Applications of Analysis

Volume 20 (2013)

Number 3

Global well-posedness for deconvolution magnetohydrodynamics models with fractional regularization

Pages: 211 – 236

DOI: http://dx.doi.org/10.4310/MAA.2013.v20.n3.a1

Author

Hani Ali (MAP5, CNRS UMR 8145, Université Paris Descartes, Paris, France)

Abstract

In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and uniqueness of solutions of the Approximate Deconvolution MHD model with magnetic diffusivity, but without kinematic viscosity. In each case, we give the optimal value of regularizations where we can prove global existence and uniqueness of the solutions. The second model includes the Approximate Deconvolution Euler Model as a particular case. Finally, an asymptotic stability result is shown in the double viscous case with weaker condition on the regularization parameter.

Keywords

magnetohydrodynamics, turbulence simulation and modeling, large-eddy simulations, partial differential equations

2010 Mathematics Subject Classification

35Q30, 76B03, 76D03, 76D05, 76F65, 76W05

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