Ill-posedness conjecture for the two-dimensional Schrödinger equation with an L1+L∞L^1+L^\inftyL1+L∞ potential
Ill-posedness conjecture. For any γ∈R\gamma\in \mathbb{R}γ∈R, there exists η∈Lx1+Lx∞(R2)\eta \in L_x^1+L_x^{\infty}(\mathbb{R}^2)η∈Lx1+Lx∞(R2) such that (eq:NLS) is ill-posed in Hxγ(R2)H_x^\gamma(\mathbb{R}^2)Hxγ(R2).
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