2021/05/13 by Fei Jiang, Song Jiang, Jiang, Fei +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2105.06080
openalex publication_date 2021/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The two-dimensional (2D) existence result of global(-in-time) solutions for the motion equations of incompressible, inviscid, non-resistive magnetohydrodynamic (MHD) fluids with velocity damping had been established in [Wu--Wu--Xu, SIAM J. Math. Anal. 47 (2013), 2630--2656]. This paper further studies the existence of global solutions for the three-dimensional (a dimension of real world) initial-boundary value problem in a horizontally periodic domain with finite height. Motivated by the multi-layers energy method introduced in [Guo--Tice, Arch. Ration. Mech. Anal. 207 (2013), 459--531], we develop a new type of two-layer energy structure to overcome the difficulty arising from three-dimensional nonlinear terms in the MHD equations, and thus prove the initial-boundary value problem admits a unique global solution. Moreover the solution has the exponential decay-in-time around some rest state. Our two-layer energy structure enjoys two features: (1) the lower-order energy (functional) can not be controlled by the higher-order energy. (2) under the a priori smallness assumption of lower-order energy, we first close the higher-order energy estimates, and then further close the lower-energy estimates in turn.