Blow-up of non-radial solutions for the L2 critical inhomogeneous NLS equation

We consider the L-2 critical inhomogeneous nonlinear Schrodinger equation in R-N i partial derivative(t)u + Delta u + vertical bar x vertical bar(-b) vertical bar u vertical bar(4-2b/N) u = 0, where N >= 1 and 0 < b < min{2, N}. We prove that if u(0) is an element of H-1 (R-N) satisfies E[u(0)] < 0, then the corresponding solution blows-up in finite time. This is in sharp contrast to the classical L-2 critical nonlinear Schrodinger equation where this type of result is only known in the radial case for N >= 2.