Research

The Boussinesq equations describe fluid-buoyancy interactions generated by differences in temperature or density. This study classifies radially homogeneous stationary self-similar solutions of the two-dimensional Boussinesq equations in a half-plane. Depending on the range of the homogeneity degree, it establishes both nonexistence and existence results for such solutions. In particular, in a low-regularity setting, it proves the existence of solutions with the same scaling as a singularity-forming profile recently obtained through numerical computation.