2D Voigt Boussinesq Equations

TL;DR

This paper investigates a regularized version of the 2D incompressible Boussinesq system, proving the existence, uniqueness, and convergence of smooth solutions under Voigt regularization, including subcritical and supercritical cases.

Contribution

It introduces and analyzes a critical Voigt regularization for the 2D Boussinesq system, establishing global well-posedness and convergence results.

Findings

Existence and uniqueness of global smooth solutions for the regularized system.

Convergence of solutions to the classical Boussinesq system as regularization is removed.

Global smooth solutions also exist for mixed subcritical-supercritical regularizations.

Abstract

We consider a critical conservative Voigt regularization of the 2D incompressible Boussinesq system on the torus. We prove the existence and uniqueness of global smooth solutions and their convergence in the smooth regime to the Boussinesq solution when the regularizations are removed. We also consider a range of mixed (subcritical-supercritical) Voigt regularizations for which we prove the existence of global smooth solutions.