2020/07/29 by Dimitri Cobb, Francesco Fanelli, Cobb, Dimitri +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2007.15094
openalex publication_date 2020/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is twofold. On the one hand, we introduce a\nquasi-homogeneous version of the classical ideal MHD system and study its\nwell-posedness in critical Besov spaces Bsp,r(\ℝd), d\≥2,\nwith 1<p<+\∞ and under the Lipschitz condition s>1+d/p and\nr\∈[1,+\∞], or s=1+d/p and r=1. A key ingredient is the\nreformulation of the system \via the so-called Els "asser variables. On\nthe other hand, we give a rigorous justification of quasi-homogeneous MHD\nmodels, both in the ideal and in the dissipative cases: when d=2, we will\nderive them from a non-homogeneous incompressible MHD system with Coriolis\nforce, in the regime of low Rossby number and for small density variations\naround a constant state. Our method of proof relies on a relative entropy\ninequality for the primitive system, and yields precise rates of convergence,\ndepending on the size of the initial data, on the order of the Rossby number\nand on the regularity of the viscosity and resistivity coefficients.\n