On the Chorin method for thermal convection equations for viscous incompressible fluids (Regularity, singularity and long time behavior for partial differential equations with conservation law)

"Regularity, singularity and long time behavior for partial differential equations with conservation law". June 6-8, 2016. edited by Keiichi Kato, Mishio Kawashita, Masashi Misawa and Takayoshi Ogawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.Stability of stationary solutions of the Oberbeck Boussinesq system and the corresponding artificial compressible system is considered. The former system is obtained by a singular limit of zero artificial Mach number in the latter system. This paper overviews recent results on a relation of the stability of stationary solutions between both systems from the viewpoint of the singular perturbation