2014/10/31 by Junxiong Jia, Jigen Peng, Jia, Junxiong +3
Engineering · Mathematics · #35Q35 #76D03 #76W05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1410.8636
openalex publication_date 2014/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigative the large time decay and stability to any given global smooth solutions of the 3D incompressible inhomogeneous MHD systems. We proved that given a solution (a, u, B) of (\refmhda), the velocity field and magnetic field decay to 0 with an explicit rate, for u which coincide with incompressible inhomogeneous Navier-Stokes equations \citezhangping. In particular, we give the decay rate of higher order derivatives of u and B which is useful to prove our main stability result. For a large solutions of (\refmhda) denoted by (a, u, B), we proved that a small perturbation to the initial data still generates a unique global smooth solution and the smooth solution keeps close to the reference solution (a, u, B). Due to the coupling between u and B, we used elliptic estimates to get ‖(u, B)‖_L1(ℝ+;B2,15/2) < C, which is different to Navier-Stokes equations.