Large Discretely Self-Similar Solutions to Oberbeck-Boussinesq System with Newtonian Gravitational Field

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 on self-similar solutions. It follows the approach of Bradshaw and Tsai and finds an explicit a priori bound for the deviation from suitably revised profiles in similarity variables.