Existence and Uniqueness of the Viscous Burgers Equation Based on Ellis Model
Zhapsarbayeva L. Wei D. Bagymkyzy B. Kanguzhin B.
2025John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2025
In this paper, we investigate the existence and uniqueness of solutions to the viscous Burgers equation describing the isothermal flow of Ellis fluids. We rigorously establish the existence and uniqueness of a weak solution (Formula presented.) corresponding to initial data (Formula presented.) where (Formula presented.) and (Formula presented.) is a parameter from the Ellis model. Furthermore, to support the theoretical findings and provide insight into the solution behavior, numerical simulations are carried out using COMSOL Multiphysics 6.0.
Burgers equation , COMSOL Multiphysics , Ellis law , existence and uniqueness , non-Newtonian fluids , Sobolev space
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Department of Fundamental Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Fundamental Mathematics
Department of Mathematics
Department of Mathematics
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