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Silva, Sim\\~ao Correia","submitted_at":"2017-03-30T15:05:47Z","abstract_excerpt":"We consider the quadratic Schr\\\"odinger system\n  $$iu_t+\\Delta_{\\gamma_1}u+\\overline{u}v=0$$ $$2iv_t+\\Delta_{\\gamma_2}v-\\beta v+\\frac 12 u^2=0,$$ where $t\\in\\mathbf{R},\\,x\\in \\mathbf{R}^d\\times \\mathbf{R}$, in dimensions $1\\leq d\\leq 4$ and for $\\gamma_1,\\gamma_2>0$, the so-called elliptic-elliptic case. We show the formation of singularities and blow-up in the $L^2$-(super)critical case. 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