The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force

We investigate models of dispersive long internal waves with rotational effects, specifically the Benjamin-Ono (BO) and intermediate long wave (ILW) equations modified by the presence of the nonlocal operator $\partial_x^{-1}$, which mathematically accounts for rotational influences. We establish a local and global well-posedness theory while ensuring the unconditional uniqueness of solutions in low-regularity Sobolev-type spaces. Our approach is based on techniques introduced by Molinet and Vento in \cite{MR3397003}.