Existence and Uniqueness of the Viscous Burgers' Equation with the p-Laplace Operator

In this paper, we investigate the existence and uniqueness of solutions for the viscous Burgers' equation for the isothermal flow of power-law non-Newtonian fluids rho(partial derivative(t)u+u partial derivative(x)u)=mu partial derivative(x)(|partial derivative(x)u|(p-2)partial derivative(x)u, augmented with the initial condition u(0,x)=u0, 00, and T>0. We show that this initial boundary problem has an unique solution in the Buchner space L-2( 0,T; W-0(1,p)(0,1)) for the given set of conditions. Moreover, numerical solutions to the problem are constructed by applying the modeling and simulation package COMSOL Multiphysics 6.0 at small and large Reynolds numbers to show the images of the solutions.