Existence and continuous dependence of large solutions for the magnetohydrodynamic equa\-tions
From MaRDI portal
Publication:1412068
DOI10.1007/s00033-003-1017-zzbMath1036.35126OpenAlexW2024367672WikidataQ57386514 ScholiaQ57386514MaRDI QIDQ1412068
Publication date: 4 November 2003
Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00033-003-1017-z
Hyperbolic conservation laws (35L65) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)
Related Items
Vanishing dissipation limit of solutions to initial boundary value problem for three dimensional incompressible magneto-hydrodynamic equations with transverse magnetic field ⋮ Global small solutions to the 3D compressible viscous non-resistive MHD system ⋮ Nonlinear stability of rarefaction waves for the compressible MHD equations ⋮ On vanishing limits of the shear viscosity and Hall coefficients for the planar compressible Hall‐MHD system ⋮ Global strong solutions to the compressible magnetohydrodynamic equations with slip boundary conditions in 3D bounded domains ⋮ Global existence and optimal convergence rates of solutions for 3D compressible magneto-micropolar fluid equations ⋮ Global strong solutions to planar radiative magnetohydrodynamic equations with density-dependent viscosity and degenerate heat-conductivity ⋮ Estimation of decay rates to large-solutions of 3D compressible magnetohydrodynamic system ⋮ Global strong solution to 3D full compressible magnetohydrodynamic flows with vacuum at infinity ⋮ A regularity criterion of strong solutions to the 2D compressible magnetohydrodynamic equations ⋮ Universal attractor for nonlinear one-dimensional compressible and radiative MHD flow ⋮ Optimal large time behaviour of the 3D compressible magnetohydrodynamics equations with large initial data ⋮ A BLOW-UP CRITERION FOR 3D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM ⋮ Global existence and convergence rates of smooth solutions for the full compressible MHD equations ⋮ Uniform regularity estimates and inviscid limit for the compressible non-resistive magnetohydrodynamics system ⋮ The relaxation limit for full compressible magnetohydrodynamic flows with the Maxwell law ⋮ Blow‐up criterion for 3D viscous‐resistive compressible magnetohydrodynamic equations ⋮ Global well-posedness of strong solutions to the magnetohydrodynamic equations of compressible flows ⋮ The decay estimates for magnetohydrodynamic equations with Coulomb force ⋮ Local well-posedness of strong solutions for the nonhomogeneous MHD equations with a slip boundary conditions ⋮ Regularity and uniqueness for the 3D compressible magnetohydrodynamic equations ⋮ On global strong solutions to the 3D MHD flows with density-temperature-dependent viscosities ⋮ A blowup criterion for viscous, compressible, and heat-conductive magnetohydrodynamic flows ⋮ Local Exact Controllability for the Planar Compressible Magnetohydrodynamic Equations ⋮ On global solutions to the 3D viscous, compressible, and heat-conducting magnetohydrodynamic flows ⋮ GLOBAL WEAK SOLUTIONS OF AN INITIAL BOUNDARY VALUE PROBLEM FOR SCREW PINCHES IN PLASMA PHYSICS ⋮ Regularity of large solutions for the compressible magnetohydrodynamic equations ⋮ On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law ⋮ Energy conservation for the weak solutions to the 3D compressible magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain ⋮ Global Strong and Weak Solutions to the Initial-Boundary-Value Problem of two-dimensional Compressible MHD System with Large Initial Data and Vacuum ⋮ Vanishing shear viscosity limit in the magnetohydrodynamic equations ⋮ Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data ⋮ Weak-strong uniqueness property for the magnetohydrodynamic equations of three-dimensional compressible isentropic flows ⋮ Time periodic solutions to the three-dimensional equations of compressible magnetohydrodynamic flows ⋮ Decay rate of strong solution for the compressible magnetohydrodynamic equations with large initial data ⋮ Long-time behavior of solution to the compressible magnetohydrodynamic equations ⋮ On the Cauchy problem of 3D nonhomogeneous magnetohydrodynamic equations with density-dependent viscosity and vacuum ⋮ Decay of the compressible magnetohydrodynamic equations ⋮ On the behavior of boundary layers of one-dimensional isentropic planar MHD equations with vanishing shear viscosity limit ⋮ A new blowup criterion for strong solutions to the Cauchy problem of three-dimensional compressible magnetohydrodynamic equations ⋮ Vanishing shear viscosity in the magnetohydrodynamic equations with temperature-dependent heat conductivity ⋮ Stability of stationary solutions for inflow problem on the planar magnetohydrodynamics ⋮ Global existence and exponential stability for a 1D compressible and radiative MHD flow ⋮ Stability of weak solutions to equations of magnetohydrodynamics with Lebesgue initial data ⋮ On the global solvability and the non-resistive limit of the one-dimensional compressible heat-conductive MHD equations ⋮ Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data ⋮ Global existence of 2D nonhomogeneous incompressible magnetohydrodynamics with vacuum ⋮ Well-posedness to the compressible viscous magnetohydrodynamic system ⋮ A blow-up criterion for 3D non-resistive compressible magnetohydrodynamic equations with initial vacuum ⋮ Global solution to the one-dimensional equations for a self-gravitating thermal radiative magnetohydrodynamics ⋮ A remark on blow-up criterion for 3D compressible magnetohydrodynamic flows with vacuum ⋮ Global existence and uniqueness of strong solutions for the magnetohydrodynamic equations ⋮ Global existence of solution for thermally radiative magnetohydrodynamic equations with the displacement current ⋮ Global existence of strong solutions to MHD with density-depending viscosity and temperature-depending heat-conductivity in unbounded domains ⋮ A free boundary problem for planar compressible Hall-magnetohydrodynamic equations ⋮ Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamic equations ⋮ Global well-posedness to the one-dimensional model for planar non-resistive magnetohydrodynamics with large data and vacuum ⋮ Asymptotic stability of stationary solutions for magnetohydrodynamic equations ⋮ Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum ⋮ The stability of contact discontinuity for compressible planar magnetohydrodynamics ⋮ Global variational solutions to the compressible magnetohydrodynamic equations ⋮ Global solutions to the three-dimensional full compressible magnetohydrodynamic flows ⋮ Stability of composite wave for inflow problem on the planar magnetohydrodynamics ⋮ Global strong solution for the full MHD equations with vacuum and large data ⋮ Global existence of large solutions to the planar magnetohydrodynamic equations with zero magnetic diffusivity ⋮ Unnamed Item ⋮ Existence and uniqueness of steady solutions to the magnetohydrodynamic equations of compressible flows ⋮ Global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations ⋮ Global strong solutions to the 1-D compressible magnetohydrodynamic equations with zero resistivity ⋮ Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations ⋮ Global existence and exponential stability of solutions for planar compressible Hall-magnetohydrodynamic equations ⋮ The Cauchy problem for the 2D magnetohydrodynamic-\(\alpha \) equations ⋮ On global solutions and asymptotic behavior of planar magnetohydrodynamics with large data ⋮ Global strong solution for compressible and radiative MHD flow with density-dependent viscosity and degenerate heat-conductivity in unbounded domains ⋮ Asymptotic stability of viscous shock profiles for compressible planar magnetohydrodynamics system ⋮ Global strong solutions to the one-dimensional heat-conductive model for planar non-resistive magnetohydrodynamics with large data ⋮ Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows ⋮ On initial boundary value problems for planar magnetohydrodynamics with large data ⋮ Decay-in-time of the highest-order derivatives of solutions for the compressible isentropic MHD equations ⋮ Global weak solutions to a 2D compressible non-resistivity MHD system with non-monotone pressure law and nonconstant viscosity ⋮ Global regularity for the Cauchy problem of three-dimensional compressible magnetohydrodynamics equations ⋮ Stability of stationary solution for the compressible viscous magnetohydrodynamic equations with large potential force in bounded domain ⋮ Large-time behavior of magnetohydrodynamics with temperature-dependent heat-conductivity ⋮ The initial value problem for the compressible magnetohydrodynamic equations without heat conductivity ⋮ Global existence and large-time behavior of weak solutions to the compressible magnetohydrodynamic equations with Coulomb force ⋮ Periodic solutions to the compressible magnetohydrodynamic equations in a periodic domain ⋮ The behavior of boundary layer for the compressible planar MHD equations at small shear viscosity ⋮ Optimal convergence rates for the strong solutions to the compressible MHD equations with potential force ⋮ Vanishing shear viscosity limit and boundary layer study for the planar MHD system ⋮ Global wellposedness of magnetohydrodynamics system with temperature-dependent viscosity ⋮ LOCAL STRONG SOLUTION TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC FLOW WITH LARGE DATA ⋮ Global strong solutions to magnetohydrodynamics with density-dependent viscosity and degenerate heat-conductivity ⋮ Optimal time‐decay rates for the 3D compressible Magnetohydrodynamic flows with discontinuous initial data and large oscillations ⋮ Energy conservation for the weak solutions to the equations of compressible magnetohydrodynamic flows in three dimensions ⋮ Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line ⋮ Global weak solutions for the Cauchy problem to one-dimensional heat-conductive MHD equations of viscous non-resistive gas ⋮ Large time behavior of the compressible magnetohydrodynamic equations with Coulomb force ⋮ On stationary solution of viscous compressible MHD equations ⋮ Long time behavior of solutions to the compressible MHD system in multi-dimensions ⋮ Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity ⋮ Global existence and convergence rates for the compressible magnetohydrodynamic equations without heat conductivity ⋮ Global axisymmetric classical solutions of full compressible magnetohydrodynamic equations with vacuum free boundary and large initial data ⋮ Global well-posedness of the non-isentropic full compressible magnetohydrodynamic equations ⋮ Global large solutions of magnetohydrodynamics with temperature-dependent heat conductivity ⋮ Global Existence for a Class of Large Solutions to Three-Dimensional Compressible Magnetohydrodynamic Equations with Vacuum