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On the incompressible limits for the full magnetohydrodynamics flows. (English) Zbl 1242.35051
This paper studies the incompressible limits for weak solutions for the full magentohydrodynamics flows in bounded and unbounded domains. In the model, various physically acceptable assumptions are made, e.g., the viscous stress tension is determined through Newton’s rheological law, the heat flux is given by Fourier’s law etc., and a scaling of the dimensionless parameters of the Mach, Froude and Alfven number is assumed according to which Ma=ϵ, Fr=ϵ, Al=ϵ where ϵ is small. A variational formulation is provided for the full problem and specific conditions for the data of the problem so that this formulation holds are stated. The limit as ϵ0 is studied in great detail in both bounded and unbounded domains.
MSC:
35B40Asymptotic behavior of solutions of PDE
76N10Compressible fluids, general
35B45A priori estimates for solutions of PDE
76W05Magnetohydrodynamics and electrohydrodynamics
35Q35PDEs in connection with fluid mechanics
35B25Singular perturbations (PDE)
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