On The Continuous Periodic Weak Slution of Boussinesq Equations

TL;DR

This paper proves the existence of continuous periodic weak solutions for the Boussinesq equations, demonstrating energy conversions and satisfying prescribed energy properties, advancing understanding of thermodynamics and fluid dynamics coupling.

Contribution

It introduces new existence results for continuous periodic weak solutions of the Boussinesq equations with prescribed energy conditions.

Findings

Existence of continuous periodic weak solutions established.

Solutions satisfy prescribed kinetic energy or other properties.

Results illustrate energy conversion between internal and mechanical energy.

Abstract

The Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics. We show the existence of continuous periodic weak solutions of the Boussinesq equations which satisfies the prescribed kinetic energy or some other prescribed property. Our results represent the conversions between internal energy and mechanical energy.