Time-decay solutions of the initial-boundary value problem of rotating magnetohydrodynamic fluids

Boundary value problems

Youyi Zhao¹  Weiwei Wang¹ 

[1] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China

关键词: magnetohydrodynamic fluid;    equilibrium state;    magnetic field;    decay estimates;    rotation;   

DOI  :  10.1186/s13661-017-0845-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We have investigated an initial-boundary problem for the perturbation equations of rotating, incompressible, and viscous magnetohydrodynamic (MHD) fluids with zero resistivity in a horizontally periodic domain. The velocity of the fluid in the domain is non-slip on both upper and lower flat boundaries. We switch the analysis of the initial-boundary problem from Euler coordinates to Lagrangian coordinates under proper initial data, and get a so-called transformed MHD problem. Then, we exploit the two-tiers energy method. We deduce the time-decay estimates for the transformed MHD problem which, together with a local well-posedness result, implies that there exists a unique time-decay solution to the transformed MHD problem. By an inverse transformation of coordinates, we also obtain the existence of a unique time-decay solution to the original initial-boundary problem with proper initial data.

【 授权许可】

CC BY