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In general, the resistivity is inversely proportional to the electrical conductivity and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, the global well-posedness of strong solution to the one-dimensional compressible, viscous, heat-conductive, non-resistive magnetohydrodynamics equations with large data, and general heat-conductivity is proved. Moreover, the non-resistive limit is justified and the convergence rates in L2-norm are obtained, provided the heat-conductivity satisfies some growth condition. [ABSTRACT FROM AUTHOR]

We study the Cauchy problem of three-dimensional compressible barotropic Navier--Stokes equations with large external potential forces. We first prove that the Cauchy problem has a unique global strong solution with large oscillations and interior vacuum, provided the initial data are of small energy and the unique steady state is strictly away from vacuum. Next, we show that if the initial data are more regular and satisfy some additional compatibility conditions, the strong solution is indeed a classical one away from the initial time. Finally, as by-products, the global existence and large-time behavior of weak solutions with large external potential forces and discontinuous initial data containing vacuum are also obtained. [ABSTRACT FROM AUTHOR]

We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic magnetohydrodynamic (MHD) flows. The non-resistive limit of the global solutions with large data is justified. As a by-product, the global well-posedness of the compressible non-resistive MHD equations is established. Moreover, the thickness of the magnetic boundary-layer of the value with is proved, where is the resistivity coefficient. The proofs of these results are based on a full use of the so-called ‘effective viscous flux’, the material derivative and the structure of the equations. [ABSTRACT FROM AUTHOR]