On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conduction

2017/05/17 by Xin Zhong, Zhong, Xin · 1 citation
Engineering · Mathematics · #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.1705.06606

openalex publication_date 2017/05/17 · openalex created_date 2017/05/26 · openalex updated_date 2026/07/28

Abstract

We are concerned with the formation of singularity and breakdown of strong solutions to the Cauchy problem of the three-dimensional full compressible magnetohydrodynamic equations with zero heat conduction. It is proved that for the initial density allowing vacuum, the strong solution exists globally if the deformation tensor \mathfrakD(u) and the pressure P satisfy ‖\mathfrakD(u)‖_{L¹(0,T;L^∞)}+‖P‖_{L^∞(0,T;L^∞)}

Cited by

• Global well-posedness of the three-dimensional non-isentropic compressible magnetohydrodynamic equations under a scaling-invariant smallness condition

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