Blowup in the nonlinear Schrödinger equation near critical dimension (Q1604263)

This paper deals with the cubic nonlinear Schrödinger equation with initial conditions \(\Phi(x,0)= \Phi_0(x)\), where \(x\in\mathbb{R}^d\) and \(2<d\leq 4\). More precisely, the authors study the case when \(d\) is algebraically close to 2. In particular, they study the values of \(d\) for which \(d-2=a^l\), for every \(l>0\), where \(a\) is a small parameter. The main result is the construction of a locally unique, monotonically decreasing in modulus, self-similar solution connecting 0 to \(\infty\).