  In the context of secular evolution, we describe the dynamics of the
radiative core of low-mass stars to understand the internal transport of
angular momentum in such stars which results in a solid rotation in the Sun
from 0.7R_sun to 0.2R_sun and a weak radial core-envelope differential rotation
in solar-type stars. This study requires at least a 2D description to capture
the latitudinal variations of the differential rotation. We build 2D numerical
models of a radiative core on the top of which we impose a latitudinal shear so
as to reproduce a cylindrical differential rotation in a convective envelope.
We perform a systematic study over the Rossby number measuring the latitudinal
differential rotation at the radiative-convective interface. The imposed shear
generates a geostrophic flow implying a cylindrical differential rotation. When
compared to the baroclinic flow that arises from the stable stratification, we
find that the geostrophic flow is dominant when the Rossby number is high
enough with a cylindrical rotation profile. For low Rossby numbers, the
baroclinic solution dominates with a quasi-shellular rotation profile. Using
scaling laws from 3D simulations, we show that slow rotators are expected to
have a cylindrical rotation profile. Fast rotators may have a shellular profile
at the beginning of the main-sequence in stellar radiative zones. This study
enables us to predict different types of differential rotation and emphasizes
the need of a new generation of 2D rotating stellar models developed in synergy
with 3D numerical simulations. The shear induced by a surface convective zone
has a strong impact on the dynamics of the underlying radiative zone in
low-mass stars. But, it cannot produce a flat internal rotation profile in a
solar configuration calling for additional processes for the transport of
angular momentum in both radial and latitudinal directions.
