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arXiv · 2512.07147

Recent Results On The Modulated Cubic Nonlinear Schr\"odinger Equation On $\mathbb{T}^2$

Josh Messing
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Abstract

New Strichartz estimates for the modulated cubic nonlinear Schr\"{o}dinger equation are proved. These Strichartz estimates allow us to show that this equation is pathwise locally well-posed. We also show that improved Strichartz estimates are available in the case where the modulation is white noise. Additionally, we comment on a few basic properties of the modulated cubic nonlinear Schr\"{o}dinger equation such as conservation of mass and convergence of its linear flow as time tends to zero.

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Josh Messing. 2025-12-08. Recent Results On The Modulated Cubic Nonlinear Schr\"odinger Equation On $\mathbb{T}^2$. https://arxiv.org/abs/2512.07147

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