“…In spite of a large literature on (S-iB) and (Z) in the whole space-time R×R n (see [3,[10][11][12]34,[43][44][45][46] for (S-iB) and [1,2,4,5,13,[16][17][18][19][20][24][25][26]28,29,35,36,[39][40][41][42] for (Z)), there are few papers treating those systems in R×Ω (see [1,33,[48][49][50] for (Z)). A major reason consists in the lack of the Fourier transform, by which Strichartz estimates, Bourgain's method, and I-method are available.…”