  The superfield models with the partial spontaneous breaking of the global
D=3, N=2 supersymmetry are discussed. The abelian gauge model describes
low-energy interactions of the real scalar field with the 3D vector and fermion
fields. We introduce the new Goldstone-Maxwell representation of the 3D gauge
superfield and show that the partial spontaneous breaking N=2 to N=1 is
possible for the non-minimal self-interaction of this modified gauge superfield
including the linear Fayet-Iliopoulos term. The dual description of the partial
breaking in the model of the self- interacting Goldstone chiral superfield is
also considered. These models have the constant vacuum solutions and describe,
respectively, the interactions of the N=1 Goldstone multiplets of the D2-brane
or supermembrane with the additional massive multiplets.
