具有非消失边界条件的四维能量临界随机非线性Schrödinger方程的全局适定性

Pub Date : 2019-10-07 DOI:10.1619/fesi.65.287

Kelvin Cheung, Guopeng Li

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引用次数: 1

摘要

考虑了$\mathbb R^4$上具有加性噪声的能量临界随机三次非线性薛定谔方程，并考虑了空间无穷远处的非消失边界条件。通过将该方程看作是$\mathbb R^4$上能量临界三次非线性薛定谔方程的扰动，我们证明了该方程在能量空间中的全局适定性。此外，我们还建立了解在能量空间上的无条件唯一性。

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Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition

We consider the energy-critical stochastic cubic nonlinear Schrodinger equation on $\mathbb R^4$ with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrodinger equation on $\mathbb R^4$, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.

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