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

Lyailya Zhapsarbayeva, Dongming Wei, Bagyzhan Bagymkyzy

Mathematics, 2025

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DOI 10.3390/math13050708
Data confidence 85 high
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Abstract

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 ρ(∂tu+u∂xu)=μ∂x∂xup−2∂xu, augmented with the initial condition u(0,x)=u0, 0 0, and T>0. We show that this initial boundary problem has an unique solution in the Buchner space L20,T;W01,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.