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

Lyailya Zhapsarbayeva, Dongming Wei and Bagyzhan Bagymkyzy ()
Additional contact information
Lyailya Zhapsarbayeva: Department of Fundamental Mathematics, L.N. Gumilyov Eurasian National University, 2, Satbaev St., Astana 010000, Kazakhstan
Dongming Wei: Department of Mathematics, Nazarbayev University, 53, Kabanbay batyr Ave., Astana 010000, Kazakhstan
Bagyzhan Bagymkyzy: Department of Fundamental Mathematics, L.N. Gumilyov Eurasian National University, 2, Satbaev St., Astana 010000, Kazakhstan

Mathematics, 2025, vol. 13, issue 5, 1-14

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 ( ∂ t u + u ∂ x u ) = μ ∂ x ∂ x u p − 2 ∂ x u , augmented with the initial condition u ( 0 , x ) = u 0 , 0 < x < L , and the boundary condition u ( t , 0 ) = u ( t , L ) = 0 , where ρ is the density, μ the viscosity, u the velocity of the fluid, 1 < p < 2 , L > 0 , 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.

Keywords: p -Laplacian; power-law non-Newtonian fluid model; existence and uniqueness; Burgers’ equation; Bochner space; Sobolev space; COMSOL Multiphysics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/708/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/708/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:708-:d:1597136

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().