2009/10/18 by Adam Larios, Larios, Adam, Edriss S. Titi +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q30 #76A10 #76B03 #76D03 #76F20 #76F55 #76F65 #76W05 #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35Q30 #msc:76A10 #msc:76B03 #msc:76D03 #msc:76F20 #msc:76F55 #msc:76F65 #msc:76W05
paper · pdf · doi:10.48550/arxiv.0910.3354
openalex publication_date 2009/10/18 · arxiv created 2010/02/11 · arxiv updated 2010/02/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We prove higher-order and a Gevrey class (spatial analytic) regularity of solutions to the Euler-Voigt inviscid α-regularization of the three-dimensional Euler equations of ideal incompressible fluids. Moreover, we establish the convergence of strong solutions of the Euler-Voigt model to the corresponding solution of the three-dimensional Euler equations for inviscid flow on the interval of existence of the latter. Furthermore, we derive a criterion for finite-time blow-up of the Euler equations based on this inviscid regularization. The coupling of a magnetic field to the Euler-Voigt model is introduced to form an inviscid regularization of the inviscid irresistive magneto-hydrodynamic (MHD) system. Global regularity of the regularized MHD system is also established.