Singular solutions of the subcritical nonlinear Schrodinger equation

We show that the subcritical $d$-dimensional nonlinear Schrödinger equation $i ψ_t + Δψ+ |ψ|^{2 σ} ψ= 0$, where $1<σd<2$, admits smooth solutions that become singular in~$L^p$ for $p^*<p \le \infty$, where $p^*:=\frac{σd}{σd -1}$. Since $\lim_{σd \to 2-} p^* = 2$, these solutions can collapse at any $2<p \le \infty$, and in particular for $p = 2 σ+2$.

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