  We consider a superconductor-two dimensional topological insulator-
superconductor junction (S-2DTI-S) and study how the 2{\pi}- and
4{\pi}-periodic Josephson currents are affected by the electron-electron
interaction. In the long-junction limit the supercurrent can by evaluated by
modeling the system as a helical Luttinger liquid coupled to superconducting
reservoirs. After having introduced bosonization in the presence of the parity
constraint we turn to consider the limit of perfect and poor interfaces. For
transparent interfaces, where perfect Andreev reflections occur at the
boundaries, the Josephson current is marginally affected by the interaction. On
the contrary, if strong magnetic scatterers are present in the weak link, the
situation changes dramatically. Here Coulomb interaction plays a crucial role
both in low and high temperature regimes. Furthermore, a phase-shift of
Josephson current can be induced by changing the direction of the magnetization
of the impurity.
