Analytic theory for three‑dimensional convectons and related (1+2)D localized patterns

Develop rigorous analytical results establishing existence, bifurcation structure (including potential snaking or slanted snaking), and stability for three‑dimensional localized convectons and multiconvectons in convection and magnetohydrodynamics models, such as binary fluid and doubly diffusive convection.

Background

Three‑dimensional convectons—localized convection cells embedded in quiescent states—have been extensively computed numerically in binary fluid and doubly diffusive convection, often exhibiting snaking‑type organization.

Despite significant numerical advances, there is no rigorous analytical existence and bifurcation theory for these 3D localized states.