Boundedness and Time Decay of Solutions to a Full Compressible Hall-MHD System

Stability near equilibrium to the full compressible magnetohydrodynamic equations

“…Due to their broad physical applications, complexity, rich phenomena and mathematical challenges, the MHD equations have recently attracted considerable interests. See [1], [2], [4], [6]- [13], [15], [16], [18]- [52], [54]- [56] and the references therein. In particular, taking the temperature into consideration, the problem becomes more complicated.…”

On vanishing limits of the shear viscosity and Hall coefficients for the planar compressible Hall‐MHD system

“…Xiang 32 established the smooth solution of the compressible Hall‐magnetohydrodynamics system converges to the solution of the compressible magneto‐hydrodynamics system as the Hall coefficient to zero. For the compressible non‐isentropic case, local well‐posedness and blow‐up criteria and the time decay of smooth solutions were established in 33,34 . Then, Lai‐Xu‐Zhang proved the long‐time existence and the optimal decay rates of solutions with the initial data sufficiently close to the non‐vacuum equilibrium in H 1 , and the vanishing limit of Hall coefficient is also justified in 27 …”

“…For the compressible non-isentropic case, local well-posedness and blow-up criteria and the time decay of smooth solutions were established in. 33,34 Then, Lai-Xu-Zhang proved the long-time existence and the optimal decay rates of solutions with the initial data sufficiently close to the non-vacuum equilibrium in H 1 , and the vanishing limit of Hall coefficient is also justified in. 27 Motivated by the results as in, 18,19,27,32 the aim of this paper is to study the vanishing limits of the shear viscosity and Hall coefficients for the planar compressible Hall-MHD system (1.1) on (0, 1) × (0, T) with the following initial and boundary conditions:…”

Decay Rates of the Full Compressible Hall-MHD Equations for Quantum Plasmas

“…The MHD systems have been studied by many authors (see [25]- [30]). For the corresponding full compressible MHD model, we can refer to [31] [32] [33] [34] [35] and references therein. Hu and Wang [31] constructed the solution of the initial-boundary value problem and established the global weak solutions.…”

“…The global smooth solutions and their decay were given by Pu and Guo in [33]. He et al [35] considered boundedness and time decay of the higher-order spatial derivatives of the smooth solutions for a full compressible Hall-MHD system.…”