Temperature patches for the subcritical Boussinesq-Navier-Stokes System with no diffusion

In this paper, we prove that temperature patch solutions to the subcritical Boussinesq-Navier-Stokes System with no diffusion preserve the H"older regularity of their boundary for all time, which generalises the previously known result by F. Gancedo and E. Garc'ia-Ju'arez [Annals of PDE, 3(2):14, 2017] to the full range of subcritical viscosity.