Uniqueness of M.H.D. thermodiffusive mixture flows with hall and ion-slip effects

A class of global large, smooth solutions for the magnetohydrodynamics with Hall and ion‐slip effects

“…It is quite rare to prove the existence of large, smooth, global solutions for quasilnear system. Under a class of large initial data, we found some results for incompressible Navier-Stokes equations, the incompressible MHD equations, and the incompressible Hall-MHD equations; see previous studies 8,9,11,13,18,[24][25][26][27][28][29][30][31][32][33][34][35][36] for details. Those motivate us to study the global well-posedness of the Cauchy problem of Equation (1.1) with large initial data.…”

On the blow-up criterion of strong solutions for the MHD equations with the Hall and ion-slip effects in $${\mathbb{R}^{3}}$$ R 3

“…Refer to [19][20][21]. Recently, Chae and Lee [2] established an existence result on strong solutions and proved the following regularity criteria Very recently, the local well posedness of the strong solution to the incompressible magnetohydrodynamic equations with the Hall and ion-slip effects was established for the whole space R 3 by Fan et al [12] and they proved that if…”

On an initial boundary-value problem for the equation of magnetohydrodynamics with the hall and ion-slip effects

“…The questions of uniqueness and of stability of for solutions of some initial boundary-value problems for Eqs. (1.2) are studied in [4][5][6][7][8][9][10], but the existence of a solution of problem (1.2), (1.3), close to a stationary solution, is established only in [8,9] in the case Jl = 0 (in [9] it is also required at the investigation of linear and nonlinear evolution problems that the Hall constant ~ is positive and sufficiently small). The 4,2 solution is found in the space W 2 (QT) which imposes additional restrictions on the compatibility of initial and boundary conditions; there appear compatibility conditions that contain the time derivative of the solution (they are not written explicitly).…”