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

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.

Tai-Peng Tsai works on the analysis of fluid and dispersive partial differential equations. His works include the regularity problem, discretely self-similar solutions, and local energy solutions of Navier-Stokes equations, the asymptotic behavior of multi-solitons of Schroedinger and gKdV equations, and the regularity of energy critical Schroedinger maps. His recent interests include the boundary bahavior of Stokes flows with the Navier boundary condition, and regularity of elliptic systems with critical drifts.