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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 Lai (Arch Ration Mech Anal 199(3):739–760, 2011). Our analysis on the the polygonal-like domains essentially relies on the recent elliptic regularity results for such domains proved in Bardos et al. (J Math Anal Appl 407(1):69–89, 2013) and Di Plinio (SIAM J Math Anal 47(1):159–178, 2015).

The 2D Euler–Boussinesq Equations in Planar Polygonal Domains with Yudovich’s Type Data