Remarks on the three and two and a half dimensional Hall-magnetohydrodynamics system: deterministic and stochastic cases

DOI10.1007/s40627-019-0033-5zbMath1468.35158OpenAlexW2941972261WikidataQ128129996 ScholiaQ128129996MaRDI QIDQ830388

Kazuo Yamazaki

Publication date: 7 May 2021

Published in: Complex Analysis and its Synergies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40627-019-0033-5

zbMATH Keywords

noisefractional LaplacianHall-magnetohydrodynamics system

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) White noise theory (60H40) Magnetohydrodynamics and electrohydrodynamics (76W05) Many-body theory; quantum Hall effect (81V70) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Regularization by noise (60H50)

Related Items (10)

Ergodicity of Galerkin approximations of surface quasi-geostrophic equations and Hall-magnetohydrodynamics system forced by degenerate noise ⋮ On the continuation principle of local smooth solution for the Hall-MHD equations ⋮ Martingale solutions of the stochastic Hall-magnetohydrodynamics equations on \(\mathbb{R}^3\) ⋮ A new boundary condition for the Hall-magnetohydrodynamics equation with the ion-slip effect ⋮ A note on the applications of Wick products and Feynman diagrams in the study of singular partial differential equations ⋮ On the well-posedness of the Hall-magnetohydrodynamics with the ion-slip effect ⋮ Global existence and asymptotic stability of 3D generalized magnetohydrodynamic equations ⋮ Logarithmically improved regularity criterion for the 3D Hall-MHD equations ⋮ Markov selections for the magnetohydrodynamics and the Hall-magnetohydrodynamics systems ⋮ Remarks on the global regularity issue of the two-and-a-half-dimensional Hall-magnetohydrodynamics system

Cites Work

• Unnamed Item
• Unnamed Item
• Singularity formation for the incompressible Hall-MHD equations without resistivity
• On global regularity of 2D generalized magnetohydrodynamic equations
• On the global regularity of two-dimensional generalized magnetohydrodynamics system
• Global Cauchy problem of 2D generalized MHD equations
• Kinetic formulation and global existence for the Hall-magneto-hydrodynamics system
• On partial regularity for the steady Hall magnetohydrodynamics system
• On the stochastic quasi-linear symmetric hyperbolic system
• The Bénard problem with random perturbations: Dissipativity and invariant measures
• Well-posedness for Hall-magnetohydrodynamics
• Local well-posedness for the Hall-MHD equations with fractional magnetic diffusion
• Dissipativity and invariant measures for stochastic Navier-Stokes equations
• On hydromagnetic waves in atmospheres with application to the Sun
• Stochastic Navier-Stokes equations: Analysis of the noise to have a unique invariant measure
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Ergodicity of the 2-D Navier-Stokes equation under random perturbations
• A remark on global regularity of 2D generalized magnetohydrodynamic equations
• Remarks on global regularity of 2D generalized MHD equations
• Well-posedness of Hall-magnetohydrodynamics system forced by Lévy noise
• Two examples on the property of the noise in the systems of equations of fluid mechanics
• Global regularity of 2D generalized MHD equations with magnetic diffusion
• Stochastic Hall-magneto-hydrodynamics system in three and two and a half dimensions
• Global regularity of the two-dimensional incompressible generalized magnetohydrodynamics system
• On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations
• Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations
• Bifurcation analysis of magnetic reconnection in Hall-MHD-systems
• Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation
• On the temporal decay for the Hall-magnetohydrodynamic equations
• Vorticity and Incompressible Flow
• Some mathematical questions related to the mhd equations
• Studies on Magneto-Hydrodynamic Waves and other Anisotropic wave motions
• Malliavin calculus for the stochastic 2D Navier—Stokes equation
• Lévy Processes and Stochastic Calculus
• Commutator estimates and the euler and navier-stokes equations
• On the global regularity issue of the two-dimensional magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian
• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
• On Partial Regularity for the 3D Nonstationary Hall Magnetohydrodynamics Equations on the Plane
• On the spontaneous magnetic field in a conducting liquid in turbulent motion
• The invariant theory of isotropic turbulence in magneto-hydrodynamics
• Stochastic Burgers' equation

This page was built for publication: Remarks on the three and two and a half dimensional Hall-magnetohydrodynamics system: deterministic and stochastic cases