What question did this study set out to answer?

This research aims to explore the existence of weak solutions for a specific fluid model involving nonlinear viscosity.

April 3, 2026

On Weak Solvability for the Navier–Stokes–Voigt Thermal Model with Nonlinear Viscosity Coefficient

Key Points

This research aims to explore the existence of weak solutions for a specific fluid model involving nonlinear viscosity.
Studied an initial–boundary value problem for a Navier–Stokes–Voigt fluid model.
Considered nonlinear viscosity and temperature impact in the model.
Employed topological approximation approaches along with an iterative process for proof.
Demonstrated the existence of weak solutions under the considered model.
Showed that incorporating nonlinear viscosity affects fluid behavior.
Highlighted the role of energy balance in the equations governing fluid motion.

Abstract

The existence of weak solutions to the initial–boundary value problem for the mathematical model describing the motion of a nonlinearly elastically retarded Navier–Stokes–Voigt fluid is studied in this paper. In this model, the fluid viscosity is considered as a nonlinear function. In addition, the temperature is also taken into account, which leads to the emergence of an additional energy balance equation. The proof is based on the topological approximation approach to the study of hydrodynamic problems, as well as the following iterative process.

Bookmark

On Weak Solvability for the Navier–Stokes–Voigt Thermal Model with Nonlinear Viscosity Coefficient

Key Points

Abstract

Cite This Study