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

Zhapsarbayeva L. Wei D. Bagymkyzy B.
March 2025 Multidisciplinary Digital Publishing Institute (MDPI)

Mathematics
2025 #13 Issue 5

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 (Formula presented.) augmented with the initial condition (Formula presented.), (Formula presented.), and the boundary condition (Formula presented.), where (Formula presented.) is the density, (Formula presented.) the viscosity, u the velocity of the fluid, (Formula presented.), (Formula presented.), and (Formula presented.). We show that this initial boundary problem has an unique solution in the Buchner space (Formula presented.) 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.

Bochner space , Burgers’ equation , COMSOL Multiphysics , existence and uniqueness , p-Laplacian , power-law non-Newtonian fluid model , Sobolev space

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Department of Fundamental Mathematics, L.N. Gumilyov, Eurasian National University, 2, Satbaev St., Astana, 010000, Kazakhstan
Department of Mathematics, Nazarbayev University, 53, Kabanbay batyr Ave., Astana, 010000, Kazakhstan

Department of Fundamental Mathematics
Department of Mathematics

10 лет помогаем публиковать статьи Международный издатель

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