We study the evolution of planet-induced vortices in radially stratified disks, with initial conditions allowing for radial buoyancy. For this purpose we run global two-dimensional hydrodynamical simulations, using the PLUTO code. Planet-induced vortices are a product of the Rossby wave instability (RWI) triggered in the edges of a planetary gap. In this work we assess the influence of radial buoyancy for the development of the vortices. We found that radial buoyancy leads to smoother planetary gaps, which generates weaker vortices. This effect is less pronounced for locally isothermal and quasi-isothermal (very small cooling rate) disks. We observed the formation of two generations of vortices. The first generation of vortices is formed in the outer wall of the planetary gap. The merged primary vortex induces accretion, depleting the mass on its orbit. This process creates a surface density enhancement beyond the primary vortex position. The second generation of vortices arise in this surface density enhancement, indicating that the bump in this region is sufficient to trigger the RWI. The merged secondary vortex is a promising explanation for the location of the vortex in the Oph IRS 48 system. Finally, we observed a nonmonotonic behavior for the vortex lifetimes as a function of the thermal relaxation timescale, agreeing with previous studies. The birth times of the secondary vortices also display a nonmonotonic behavior, which is correlated with the growth time of the primary vortex and its induced accretion.