Abstract We construct a two-parameter continuum of type II blow up solutions for the energy-critical nonlinear Schrödinger equation in dimension d = 3 d = 3. The solutions collapse to a single energy bubble in finite time and have the form aligned u (t, x) = e^i (t) (t) ^1{2}W ( (t) x) + (t, x), ~ ~ t [0, T), ~ x {\, {R\, }}³, aligned u (t, x) = e i α (t) λ (t) 1 2 W (λ (t) x) + η (t, x), t ∈ [ 0, T), x ∈ R 3, where W (x) = (1 + |x|²3) ^-1{2} W (x) = (1 + | x | 2 3) - 1 2 is the ground state solution, (t) = (T -t) ^- 1{2 - } λ (t) = (T - t) - 1 2 - ν for suitable
Tobias Schmid (Mon,) studied this question.