# Evolution Boussinesq model with nonmonotone friction and heat flux boundary conditions

## TL;DR

This paper establishes the existence and regularity of solutions for a 2D Boussinesq model incorporating nonmonotone friction and heat flux boundary conditions, advancing mathematical understanding of complex fluid-thermal interactions.

## Contribution

It introduces a novel approach combining time retardation, regularization, and Galerkin methods to analyze hemivariational inequalities in fluid dynamics.

## Key findings

- Proves existence of solutions for the model.
- Establishes regularity properties of solutions.
- Extends mathematical theory to nonmonotone boundary conditions.

## Abstract

In this paper we prove the existence and regularity of a solution to a two-dimensional system of evolutionary hemivariational inequalities which describes the Boussinesq model with nonmonotone friction and heat flux. We use the time retardation and regularization technique, combined with a regularized Galerkin method, and recent results from the theory of hemivariational inequalities.