On the infinite Prandtl number limit in two-dimensional magneto-convection

TL;DR

This paper rigorously justifies the infinite Prandtl number limit in 2D magneto-convection, analyzing convergence, initial layer thickness, and constructing an effective dynamics model for initial layer behavior.

Contribution

It provides the first rigorous analysis of the infinite Prandtl number limit in 2D magneto-convection, including convergence rates and initial layer dynamics.

Findings

Convergence rates for the infinite Prandtl number limit are established.

The thickness of the initial layer is characterized.

An effective dynamics model for initial layer motion is constructed.

Abstract

In this paper, the infinite limit of the Prandtl number is justified for the two-dimensional incompressible magneto-convection, which describes the nonlinear interaction between the Rayleigh-B$\rm\acute{e}$nard convection and an externally magnetic field. Both the convergence rates and the thickness of initial layer are obtained. Moreover, based on the method of formal asymptotic expansions, an effective dynamics is constructed to simulate the motion within the initial layer.