Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data

2011/09/28 by Slim Ibrahim, Ibrahim, Slim, Tsuyoshi Yoneda +1 · 1 citation
Engineering · Mathematics · #35Q30 #76N10 #76W05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35Q30 #msc:76N10 #msc:76W05

paper · pdf · doi:10.48550/arxiv.1109.6089

arxiv created 2011/09/28 · openalex publication_date 2011/09/28 · arxiv updated 2011/09/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Existence of local-in-time unique solution and loss of smoothness of full Magnet-Hydro-Dynamics system (MHD) is considered for periodic initial data. The result is proven using Fujita-Kato's method in ℓ¹ based (for the Fourier coefficients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwells's equations. A loss of smoothness result is shown for the velocity and magnetic field. It comes from the damped-wave operator which does not have any smoothing effect.

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