Recent Results On The Modulated Cubic Nonlinear Schr\"odinger Equation On T2
Abstract
New Strichartz estimates for the modulated cubic nonlinear Schr\"odinger 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\"odinger equation such as conservation of mass and convergence of its linear flow as time tends to zero.
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