Large discretely self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field

TL;DR

This paper constructs large discretely self-similar solutions to the Oberbeck-Boussinesq system with a Newtonian gravitational field, extending previous work on self-similar solutions and providing explicit bounds on deviations.

Contribution

It introduces a method to construct large discretely self-similar solutions for the Oberbeck-Boussinesq system with gravitational effects, expanding the class of known solutions.

Findings

Constructed solutions for large initial data.

Extended previous self-similar solution frameworks.

Provided explicit bounds on solution deviations.

Abstract

Discretely self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field for large discretely self-similar initial data are constructed in this note, extending the construction of Brandolese and Karch (arXiv:2311.01093) on self-similar solutions. It follows the approach of Bradshaw and Tsai (Ann.~Henri Poincar\'e 2017) and find an explicit a priori bound for the deviation from suitably revised profiles in similarity variables.