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 L×H. 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 (u10,u20)∈L2(Ω), Ω=[0,L]×[0,H]×(0,∞). Afterward, the results are extended for (u10,u20)∈Lp(Ω), p>2. Lastly, the existence criteria are obtained when (u10,u20)∈H1(Ω). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids.