Global Existence Of Strong Solutions To The 2D Incompressible Nonhomogeneous MHD With Density-dependent Viscosity

In this thesis,we consider the incompressible 2-D nonhomogeneous MHD equations with variable viscosity and variable conductivity in a bounded domain.The governing equations of nonhomogeneous MHD can be stated as follows (?)initial conditions(?)boundary conditions Where ?(?)R2.The variables p(x,t),u(x,t)denote the fluid density,the velocity of the liquid;B is the magnetic field.P is the scalar pressure.?(?)>0 is the viscosity coefficient and v(?)>0 is the magnetic:diffusivity coefficicent.we suppose that ?(?)and v(?)are C1 functions and that for some positive constant (?).