2016/05/02 by Yuan Cai, Zhen Lei, Cai, Yuan +1 · 4 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP
paper · pdf · doi:10.48550/arxiv.1605.00439
25 pages, both 2D and 3D are considered
arxiv created 2016/05/02 · openalex publication_date 2016/05/02 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the Cauchy problem of the incompressible magnetohydrodynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initial magnetic field from a non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν≥ 0 and all space dimension n ≥ 2. Such a result holds true uniformly in nonnegative viscosity parameter. The proof is based on the inherent strong null structure of the systems which was first introduced for incompressible elastodynamics by the second author in \citeLei14 and Alinhac's ghost weight technique.