Abstract
We revisit the finite time blow-up for the fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity −|x|−2|u|4nu. By exploiting localized virial estimates and spatial decay of the nonlinearity, we prove the finite time blow-up of non-radial solutions with negative energy. Our result is the first one dealing with the existence of non-radial blow-up solutions to the fourth-order Schrödinger equations.
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