On Classical Solutions of the Compressible Magnetohydrodynamic Equations with Vacuum

DOI10.1137/14095265XzbMath1325.35176arXiv1401.2705MaRDI QIDQ5264064

Shengguo Zhu

Publication date: 20 July 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.2705

zbMATH Keywords

vacuumcompatibility conditionclassical solutionsmagnetohydrodynamicsblow-up criterion

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Blow-up in context of PDEs (35B44) Classical solutions to PDEs (35A09)

Related Items (10)

Existence for the compressible magnetohydrodynamic equations with vacuum ⋮ On local strong solutions to the 2D Cauchy problem of the compressible non-resistive magnetohydrodynamic equations with vacuum ⋮ Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data ⋮ Global small solutions to a special \(2\frac{1}{2}\)-D compressible viscous non-resistive MHD system ⋮ Global strong solutions to the compressible magnetohydrodynamic equations with slip boundary conditions in 3D bounded domains ⋮ On classical solutions to the Cauchy problem of the 2D compressible non-resistive MHD equations with vacuum states ⋮ Local well-posedness for a two-phase model with magnetic field and vacuum. ⋮ Blow-up criterion for the 3D viscous polytropic fluids with degenerate viscosities ⋮ Strong solutions to the Cauchy problem of two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction ⋮ Local well-posedness to the three-dimensional barotropic compressible magnetohydrodynamic equations with vacuum

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