  We address the well-posedness of the 2D (Euler)-Boussinesq equations with
zero viscosity and positive diffusivity in the polygonal-like domains with
Yudovich's type data, which gives a positive answer to part of the questions
raised in 2011 [Lai-Pan-Zhao, Initial boundary value problem for
two-dimensional viscous Boussinesq equations, Arch. Ration. Mech. Anal. 199
(2011), no. 3, 739-760]. Our analysis on the the polygonal-like domains
essentially relies on the recent elliptic regularity results for such domains
proved in 2013 [Bardos-Plinio-Temam, The Euler equations in planar nonsmooth
convex domains, J. Math. Anal. Appl. 407 (2013), no. 1, 69-89.] and
[Plinio-Temam, Grisvard's shift theorem near $l^\infty$ and yudovich theory on
polygonal domains, arXiv:1310.5444]
