  In this paper, we study the global in time existence problem for the
Groma-Balogh model describing the dynamics of dislocation densities. This model
is a two-dimensional model where the dislocation densities satisfy a system of
transport equations such that the velocity vector field is the shear stress in
the material, solving the equations of elasticity. This shear stress can be
expressed as some Riesz transform of the dislocation densities. The main tool
in the proof of this result is the existence of an entropy for this system
