On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics
From MaRDI portal
Publication:2442914
DOI10.1016/j.jde.2014.03.003zbMath1295.35122arXiv1305.4681OpenAlexW2004156856MaRDI QIDQ2442914
Publication date: 2 April 2014
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1305.4681
Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) First-order nonlinear hyperbolic equations (35L60) Magnetohydrodynamics and electrohydrodynamics (76W05) Blow-up in context of PDEs (35B44)
Related Items
Ergodicity of Galerkin approximations of surface quasi-geostrophic equations and Hall-magnetohydrodynamics system forced by degenerate noise ⋮ Low Mach number limit of the full compressible Hall-MHD system ⋮ Well-posedness results for the 3D incompressible Hall-MHD equations ⋮ Time-periodic and stationary solutions to the compressible Hall-magnetohydrodynamic system ⋮ Low regularity well-posedness for the 3D generalized Hall-MHD system ⋮ Regularity criterion for the 3D Hall-magneto-hydrodynamics ⋮ A remark on the blow-up criterion for the 3D Hall-MHD system in Besov spaces ⋮ 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 ⋮ Zero Mach number limit of the compressible Hall-magnetohydrodynamic equations ⋮ Local well-posedness for the Hall-MHD system in optimal Sobolev spaces ⋮ On the blow-up criterion of strong solutions for the MHD equations with the Hall and ion-slip effects in \({\mathbb{R}^{3}}\) ⋮ Local well-posedness and blow-up for the solutions to the axisymmetric inviscid Hall-MHD equations ⋮ Global well-posedness for MHD system with mixed partial dissipation and magnetic diffusion in \(2 \frac{1}{2}\) dimensions ⋮ On regularity criteria for the 3D Hall-MHD equations in terms of the velocity ⋮ Singularity formation for the incompressible Hall-MHD equations without resistivity ⋮ Well-posedness for the incompressible Hall-MHD equations in low regularity spaces ⋮ Global regularity for the 3D generalized Hall-MHD system ⋮ Global wellposedness for Hall-MHD equations ⋮ On uniqueness and helicity conservation of weak solutions to the electron-MHD system ⋮ A new regularity criterion for the 3D generalized Hall-MHD system with \(\beta \in (\frac{1}{2}, 1\)] ⋮ On well-posedness of generalized Hall-magneto-hydrodynamics ⋮ On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation ⋮ On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: Illposedness near degenerate stationary solutions ⋮ Stochastic Hall-magneto-hydrodynamics system in three and two and a half dimensions ⋮ On the local and global existence of the Hall equations with fractional Laplacian and related equations ⋮ Global wellposedness and large time behavior of solutions to the Hall-magnetohydrodynamics equations ⋮ Existence, regularity and uniqueness of weak solutions with bounded magnetic fields to the steady Hall-MHD system ⋮ On the Cauchy problem for the compressible Hall-magneto-hydrodynamics equations ⋮ Steady states of Hall-MHD system ⋮ Global well-posedness and decay characterization of solutions to 3D MHD equations with Hall and ion-slip effects ⋮ Uniform regularity for a density-dependent incompressible Hall-MHD system ⋮ Local well-posedness for the Hall-MHD equations with fractional magnetic diffusion ⋮ Regularity criteria for the incompressible Hall-magnetohydrodynamic equations ⋮ On a single-component regularity criterion for the non-resistive axially symmetric Hall-MHD system ⋮ Global well-posedness, BKM blow-up criteria and zero \(h\) limit for the 3D incompressible Hall-MHD equations ⋮ Asymptotic behavior, regularity criterion and global existence for the generalized Navier-Stokes equations ⋮ Low Mach number limit of the compressible Hall-magnetohydrodynamic system ⋮ On the well-posedness of magnetohydrodynamics system with Hall and ion-slip in critical spaces ⋮ Regularity criteria for the 3D generalized MHD and Hall-MHD systems ⋮ A new boundary condition for the Hall-magnetohydrodynamics equation with the ion-slip effect ⋮ On the blow-up criterion of smooth solutions for Hall-magnetohydrodynamics system with partial viscosity ⋮ Continuous dependence of solutions in low regularity spaces for the Hall-MHD equations ⋮ Global well-posedness for the Hall-magnetohydrodynamics system in larger critical Besov spaces ⋮ Global well-posedness of the 3D incompressible Hall-MHD equations for small initial data in certain Besov spaces ⋮ Irreducibility of the three, and two and a half dimensional Hall-magnetohydrodynamics system ⋮ On strong solutions to the compressible Hall-magnetohydrodynamic system ⋮ Long time behavior of solutions to the 3D Hall-magneto-hydrodynamics system with one diffusion ⋮ An improved regularity criterion for the 3D Hall-MHD equations via the vorticity ⋮ Beale-Kato-Madja type criteria of smooth solutions to 3D Hall-MHD flows ⋮ A remark on regularity criterion for the 3D Hall-MHD equations based on the vorticity ⋮ Global small solutions to the inviscid Hall-MHD system ⋮ On blow-up criteria for a new Hall-MHD system ⋮ On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effects ⋮ Global well-posedness for the 3D incompressible Hall-magnetohydrodynamic equations with Fujita-Kato type initial data ⋮ On partial regularity for the steady Hall magnetohydrodynamics system ⋮ On global existence, energy decay and blow-up criteria for the Hall-MHD system ⋮ A regularity criterion for the density-dependent Hall-magnetohydrodynamics ⋮ Well-posedness for the Hall-magnetohydrodynamics system in critical space ⋮ A free boundary problem for planar compressible Hall-magnetohydrodynamic equations ⋮ Global weak solutions to the density-dependent Hall-magnetohydrodynamics system ⋮ Global existence and asymptotic behavior for the 3D generalized Hall-MHD system ⋮ Global well-posedness and analyticity of solutions to three-dimensional Hall-MHD equations ⋮ A remark on the existence of a class of stretched \(2 \frac{1}{2} D\) magnetohydrodynamics flow ⋮ Regularity criteria and small data global existence to the generalized viscous Hall-magnetohydrodynamics ⋮ On the well-posedness of the Hall-magnetohydrodynamics with the ion-slip effect ⋮ Global existence and exponential stability of solutions for planar compressible Hall-magnetohydrodynamic equations ⋮ A class of large solutions to the 3D generalized Hall-MHD equations ⋮ Asymptotic stability of stationary solutions for Hall magnetohydrodynamic equations ⋮ The 3D incompressible Hall magneto-hydrodynamics equations with partial hyperdissipation ⋮ Well-posedness and long time behavior for the electron inertial Hall-MHD system in Besov and Kato-Herz spaces ⋮ Global regularity for the \(2\frac{1}{2}\)D incompressible Hall-MHD system with partial dissipation ⋮ Uniform regularity for the isentropic Hall-MHD system ⋮ Regularity criterion for the 3D Hall-magnetohydrodynamic equations involving the vorticity ⋮ A class large solution of the 3D Hall-magnetohydrodynamic equations ⋮ On 3D Hall-MHD equations with fractional Laplacians: global well-posedness ⋮ On the well-posedness and temporal decay for the 3D generalized incompressible Hall-MHD system ⋮ Insight into the significance of Hall current and Joule heating on the dynamics of Darcy-Forchheimer peristaltic flow of Rabinowitsch fluid ⋮ Logarithmically improved regularity criterion for the 3D Hall-MHD equations ⋮ Well-posedness of Hall-magnetohydrodynamics system forced by Lévy noise ⋮ The asymptotic stability of the solution to the full Hall-MHD system in \(\mathbb{R}^3\) ⋮ 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 ⋮ A single-component BKM-type regularity criterion for the inviscid axially symmetric Hall-MHD system ⋮ Blow-up of a dyadic model with intermittency dependence for the Hall MHD ⋮ Markov selections for the magnetohydrodynamics and the Hall-magnetohydrodynamics systems ⋮ On the Cauchy problem of compressible full Hall-MHD equations ⋮ On the global existence to Hall-MHD system ⋮ Remarks on the global regularity issue of the two-and-a-half-dimensional Hall-magnetohydrodynamics system ⋮ Derivation of the Hall-MHD equations from the Navier-Stokes-Maxwell equations ⋮ A note on the Liouville type theorem for the smooth solutions of the stationary Hall-MHD system ⋮ A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations ⋮ Regularity criteria for 3D Hall-MHD equations ⋮ Existence and regularity of solutions for a 3D coupled parabolic-elliptic equations related to magnetic relaxation ⋮ On the local and global existence of unique solutions to the Lüst model ⋮ Regularity criteria for the density-dependent Hall-magnetohydrodynamics ⋮ Global well-posedness for the incompressible Hall-magnetohydrodynamic system in critical Fourier-Besov spaces ⋮ Beale-Kato-Majda regularity criterion of smooth solutions for the Hall-MHD equations with zero viscosity ⋮ The 3D incompressible Hall-MHD equations: global well-posedness ⋮ Global existence and optimal decay rates of solutions for compressible Hall-MHD equations ⋮ Global regularity for the 3D axisymmetric incompressible Hall-MHD system with partial dissipation and diffusion ⋮ The global solvability of the Hall-magnetohydrodynamics system in critical Sobolev spaces ⋮ 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 origin of the energy dissipation anomaly in (Hall) magnetohydrodynamics ⋮ Decay characterization of solutions to generalized Hall-MHD system in R3 ⋮ Global smooth solutions to the 3D generalized Hall-magnetohydrodynamic equations with large data ⋮ Martingale solutions of the stochastic Hall-magnetohydrodynamics equations on \(\mathbb{R}^3\) ⋮ On the asymptotic behavior of solutions to 3D generalized Hall‐MHD equations ⋮ A class of global large, smooth solutions for the magnetohydrodynamics with Hall and ion‐slip effects ⋮ Remark on regularity criterion for the 3D Hall-MHD equations involving only the vorticity ⋮ The optimal temporal decay rates for compressible Hall-magnetohydrodynamics system ⋮ On the blow-up criterion for the Hall-MHD problem with partial dissipation in \(\mathbb{R}^3\) ⋮ Global solutions for the incompressible Hall-magnetohydrodynamics system around constant equilibrium states ⋮ On the existence and temporal asymptotics of solutions for the two and half dimensional Hall MHD ⋮ Well-posedness for the incompressible Hall-MHD system with initial magnetic field belonging to \(H^{\frac{3}{2}}(\mathbb{R}^3)\) ⋮ Global well-posedness of the incompressible Hall-MHD system in critical spaces ⋮ Decay rates of the highest order spatial derivatives for solutions of compressible Hall MHD system with or without Coulomb force ⋮ Hall effect on the asymptotic stability of the planar compressible MHD flows ⋮ Liouville type Theorems for the 3D stationary Hall‐MHD equations ⋮ Large time behavior for the Hall-MHD equations with horizontal dissipation ⋮ Unnamed Item ⋮ Applications of harmonic analysis techniques to regularity problems of dissipative equations ⋮ Global existence and large time behavior of solutions for full compressible Hall-MHD equations ⋮ GLOBAL REGULARITY FOR 3D GENERALIZED HALL MAGNETO-HYDRODYNAMICS EQUATIONS ⋮ Nonunique Weak Solutions in Leray--Hopf Class for the Three-Dimensional Hall-MHD System ⋮ On Partial Regularity for the 3D Nonstationary Hall Magnetohydrodynamics Equations on the Plane ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Space-time decay estimates for the incompressible viscous resistive MHD and Hall-MHD equations ⋮ On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system ⋮ The continuous dependence for the Hall-MHD equations with fractional magnetic diffusion ⋮ On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces ⋮ The blow-up criterion via horizontal component of velocity for the Hall-MHD equations ⋮ Space–time decay of solutions to three-dimensional MHD equations with Hall and ion-slip effects ⋮ On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics with horizontal dissipation ⋮ Energy conservation for the nonhomogeneous incompressible ideal Hall-MHD equations ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Unnamed Item
- Kinetic formulation and global existence for the Hall-magneto-hydrodynamics system
- Bilinear estimates in \(BMO\) and the Navier-Stokes equations
- On a regularity criterion for the solutions to the 3D Navier-Stokes equations.
- Global well-posedness in the super-critical dissipative quasi-geostrophic equations
- Bifurcation analysis of magnetic reconnection in Hall-MHD-systems
- On the temporal decay for the Hall-magnetohydrodynamic equations
- Vorticity and Incompressible Flow
- Studies on Magneto-Hydrodynamic Waves and other Anisotropic wave motions
- Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
- Sharp Sobolev Inequality of Logarithmic Type and the Limiting Regularity Condition to the Harmonic Heat Flow