On stability of pseudo-conformal blowup for \(L^{2}\)-critical Hartree NLS
The authors consider the \(L^2\)-critical nonlinear Schrödinger equation in \({\mathbb R}^4\) with Hartree-type (nonlocal) nonlinearity. They prove the existence of critical mass finite-time blow-up solutions \(u(t,x)\) with blow-up rate \(\|\nabla u\|_{L^2}\sim \frac{1}{|t|}\) when \(t\rightarrow 0\).
scientific article