Minimal mass blow-up solutions to rough nonlinear Schroedinger equations

Yiming Su; Deng Zhang

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arXiv · 2002.09659

Minimal mass blow-up solutions to rough nonlinear Schroedinger equations

Yiming Su·Deng Zhang

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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.

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Yiming Su, Deng Zhang. 2020-02-22. Minimal mass blow-up solutions to rough nonlinear Schroedinger equations. https://arxiv.org/abs/2002.09659

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