This paper is devoted to the study of the lifespan of the solutions of the primitive equations for less regular initial data. We interpolate the globall well-posedness results for small initial data in H1given by the Fujita-Kato theorem, and the result from [6] which gives global well-posedness if the Rossby parameter is small enough, and for regular initial data (oscillating part in H1 and H 1/2 and quasigeostrophic part in H1).