Minimal mass blow-up solutions to rough nonlinear Schroedinger equations

2020/02/22 by Yiming Su, Deng Zhang, Su, Yiming +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2002.09659

openalex publication_date 2020/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the focusing mass-critical rough nonlinear Schroedinger equations, where the stochastic integration is taken in the sense of controlled rough path. We obtain the global well-posedness if the mass of initial data is below that of the ground state. Moreover, the existence of minimal mass blow-up solutions is also obtained in both dimensions one and two. In particular, these yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up of solutions in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schroedinger equations with lower order perturbations.

Related

• A note on log-log blow up solutions for stochastic nonlinear Schrödinger equations
• Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on ℝ: small initial data
• On the multi-bubble blow-up solutions to rough nonlinear Schrödinger equations
• Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case
• Blow-up for the nonlinear Schrödinger equation with combined nonlinearities