  We are concerned with the long-time solvability for 2D inviscid Boussinesq
equations for a larger class of initial data which covers the case of
borderline regularity. First we show the local solvability in Besov spaces
uniformly with respect to a parameter $\kappa$ associated with the
stratification of the fluid. Afterwards, employing a blow-up criterion and
Strichartz-type estimates, the long-time solvability is obtained for large
$\kappa$ regardless of the size of initial data.
