Global Existence of Bounded Solutions for Eyring-Powell Flow in a Semi-Infinite Rectangular Conduct

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 (u10,u20) 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))is an element of L-2(Omega), Omega=[0,L]x[0,H]x(0,infinity). Afterward, the results are extended for (u(1)(0),u(2)(0))is an element of Lp(Omega), p>2. Lastly, the existence criteria are obtained when (u(1)(0),u(2)(0))is an element of H1(Omega). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring-Powell fluids.