2019/12/09 by Dimitri Cobb, Francesco Fanelli, Cobb, Dimitri +1 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1912.04077
openalex publication_date 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the analysis of a singular perturbation problem for\na 2-D incompressible MHD system with density variations and Coriolis force,\nin the limit of small Rossby numbers. Two regimes are considered. The first one\nis the quasi-homogeneous regime, where the densities are small perturbations\naround a constant state. The limit dynamics is identified as an incompressible\nhomogeneous MHD system, coupled with an additional transport equation for the\nlimit of the density variations. The second case is the fully non-homogeneous\nregime, where the densities vary around a general non-constant profile. In this\ncase, in the limit, the equation for the magnetic field combines with an\nunderdetermined linear equation, which links the limit density variation\nfunction with the limit velocity field. The proof is based on a compensated\ncompactness argument, which enables us to consider general ill-prepared initial\ndata. An application of Di Perna-Lions theory for transport equations allows to\ntreat the case of density-dependent viscosity and resistivity coefficients.\n