On Partial Regularity for the 3D Nonstationary Hall Magnetohydrodynamics Equations on the Plane

DOI10.1137/15M1012037zbMath1336.35287arXiv1502.03474MaRDI QIDQ5743840

Donghao Chae, Joerg Wolf

Publication date: 8 February 2016

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

Full work available at URL: https://arxiv.org/abs/1502.03474

zbMATH Keywords

partial regularitynonstationary Hall-MHD equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Weak solutions to PDEs (35D30) Hydrodynamic and hydromagnetic problems in astronomy and astrophysics (85A30) PDEs in connection with astronomy and astrophysics (35Q85)

Related Items (38)

Ergodicity of Galerkin approximations of surface quasi-geostrophic equations and Hall-magnetohydrodynamics system forced by degenerate noise ⋮ Well-posedness results for the 3D incompressible Hall-MHD equations ⋮ Regularity of the \(3D\) stationary Hall magnetohydrodynamic equations on the plane ⋮ Remarks on the three and two and a half dimensional Hall-magnetohydrodynamics system: deterministic and stochastic cases ⋮ Active vector models generalising 3D Euler and electron–MHD equations ⋮ On the continuation principle of local smooth solution for the Hall-MHD equations ⋮ On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: Illposedness near degenerate stationary solutions ⋮ On the local and global existence of the Hall equations with fractional Laplacian and related equations ⋮ Existence, regularity and uniqueness of weak solutions with bounded magnetic fields to the steady Hall-MHD system ⋮ Steady states of Hall-MHD system ⋮ A class of global large, smooth solutions for the magnetohydrodynamics with Hall and ion‐slip effects ⋮ On the blow-up criterion for the Hall-MHD problem with partial dissipation in \(\mathbb{R}^3\) ⋮ On the existence and temporal asymptotics of solutions for the two and half dimensional Hall MHD ⋮ Hall effect on the asymptotic stability of the planar compressible MHD flows ⋮ An efficient Hermite-Galerkin spectral scheme for three-dimensional incompressible Hall-magnetohydrodynamic system on infinite domain ⋮ On the global well-posedness for the compressible Hall-MHD system ⋮ Liouville type Theorems for the 3D stationary Hall‐MHD equations ⋮ Irreducibility of the three, and two and a half dimensional Hall-magnetohydrodynamics system ⋮ A remark on regularity criterion for the 3D Hall-MHD equations based on the vorticity ⋮ Global existence and large time behavior of solutions for full compressible Hall-MHD equations ⋮ Global small solutions to the inviscid Hall-MHD system ⋮ A free boundary problem for planar compressible Hall-magnetohydrodynamic equations ⋮ Global weak solutions to the density-dependent Hall-magnetohydrodynamics system ⋮ Global well-posedness and analyticity of solutions to three-dimensional Hall-MHD equations ⋮ Global existence and exponential stability of solutions for planar compressible Hall-magnetohydrodynamic equations ⋮ Global regularity for the \(2\frac{1}{2}\)D incompressible Hall-MHD system with partial dissipation ⋮ Regularity criterion for the 3D Hall-magnetohydrodynamic equations involving the vorticity ⋮ On 3D Hall-MHD equations with fractional Laplacians: global well-posedness ⋮ Logarithmically improved regularity criterion for the 3D Hall-MHD equations ⋮ Well-posedness of Hall-magnetohydrodynamics system forced by Lévy noise ⋮ Existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid ⋮ Two examples on the property of the noise in the systems of equations of fluid mechanics ⋮ Markov selections for the magnetohydrodynamics and the Hall-magnetohydrodynamics systems ⋮ On the Cauchy problem of compressible full Hall-MHD equations ⋮ Remarks on the global regularity issue of the two-and-a-half-dimensional Hall-magnetohydrodynamics system ⋮ A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations ⋮ Unnamed Item ⋮ Beale-Kato-Majda regularity criterion of smooth solutions for the Hall-MHD equations with zero viscosity

Cites Work

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