Abstract
The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring-Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions LxH. Starting from the initial velocity profiles (u(1)(0),u(2)(0)) in xy-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u(1)(0),u(2)(0))? L-2(O), O=[0,L]x[0,H]x(0,8). Afterward, the results are extended for (u(1)(0),u(2)(0),)? L-p(O), p>2. Lastly, the existence criteria are obtained when (u(1)(0),u(2)(0))? H-1(?). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring-Powell fluids.