A priori estimates and existence of real-valued periodic solutions to the modified Benjamin-Ono equation with initial data in $H^s$ for $s>1/4$ are proved locally in time. The approach relies on frequency dependent time localization, after which dispersive properties from Euclidean space are recovered. The same regularity results are proved for the cubic derivative nonlinear Schrödinger equation.

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关于 H1/2(T) 以下修正的 Benjamin-Ono 方程的先验估计和周期解的存在

初始数据为 的修正 Benjamin-Ono 方程的实值周期解的先验估计和存在性 $H^{秒}$ 为了 $秒>1/4$在当地及时证明。该方法依赖于频率相关的时间定位，之后从欧几里得空间中恢复色散特性。对于三次导数非线性薛定谔方程，证明了相同的规律性结果。