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Zbl 1242.35051
Kwon, Young-Sam; Trivisa, Konstantina
On the incompressible limits for the full magnetohydrodynamics flows. (English)
[J] J. Differ. Equations 251, No. 7, 1990-2023 (2011). ISSN 0022-0396

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 $Ma=\epsilon$, $Fr=\sqrt{\epsilon}$, $Al=\sqrt{\epsilon}$ where $\epsilon$ 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 $\epsilon \to 0$ is studied in great detail in both bounded and unbounded domains.
[Athanasios Yannacopoulos (Athens)]

MSC 2000:: *35B40 Asymptotic behavior of solutions of PDE
76N10 Compressible fluids, general
35B45 A priori estimates
76W05 Flows in presence of electromagnetic forces
35Q35 Other equations arising in fluid mechanics
35B25 Singular perturbations (PDE)

Keywords: Mach number; Froude number; Alfven number; compressible and viscous fluid; Helmholtz function

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