Abstract
Abstract In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity is considered, but the initial vacuum can be permitted inside the region. By deriving a priori ν (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for the compressible resistive MHD equations is also established.
Highlights
Introduction and Main ResultsCompressible magnetohydrodynamics (MHD) is used to describe the macroscopic behavior of the electrically conducting uid in a magnetic eld
In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at in nity is considered, but the initial vacuum can be permitted inside the region
By deriving a priori ν-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data
Summary
Compressible magnetohydrodynamics (MHD) is used to describe the macroscopic behavior of the electrically conducting uid in a magnetic eld. The system of the resistive MHD equations has the form: ρ t. Ρ, u, P(ρ) and b denote the density, velocity, pressure and magnetic eld, respectively. Μ > is the viscosity coe cient, the constant ν > is the resistivity coe cient acting as the magnetic di usion coe cient of the magnetic eld. We consider the isentropic compressible MHD equations in which the equation of the state has the form. It is well known that the resistivity coe cient ν is inversely proportional to the electrical conductivity, it is more reasonable to ignore the magnetic di usion which means ν = , when the
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