Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS

Abstract

Let $d\ge 4$ and let $u$ be a global solution to the focusing mass-critical nonlinear Schrödinger equation $i{u}_t+\Delta u=-|u{|}^{\frac{4}{d}}u$ with spherically symmetric $H_x^1$ initial data and mass equal to that of the ground state $Q$. We prove that if $u$ does not scatter then, up to phase rotation and scaling, $u$ is the solitary wave $e^{it}Q$. Combining this result with that of Merle \cite{merle2}, we obtain that in dimensions $d\ge 4$, the only spherically symmetric minimal-mass blowup solutions are, up to phase rotation and scaling, the pseudo-conformal ground state and the solitary wave.

17 pages

References in corpus (3)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Minimal-mass blowup solutions of the mass-critical NLS