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 (u 1 0 , u 2 0) in x y -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 (Ω) , Ω = [ 0 , L ] × [ 0 , H ] × (0 , ∞) . Afterward, the results are extended for (u 1 0 , u 2 0) ∈ L p (Ω) ,  p > 2 . Lastly, the existence criteria are obtained when (u 1 0 , u 2 0) ∈ H 1 (Ω) . A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids. [ABSTRACT FROM AUTHOR]