论文标题
低规律性良好，用于圆上的广义benjamin-ono方程
Low regularity well-posedness for generalized Benjamin-Ono equations on the circle
论文作者
论文摘要
显示了具有四分之一或较高非线性和周期性边界条件的广义本杰明·诺方程的新的低规律性良好性结果。我们使用短时傅立叶变换限制方法和修改能量来克服衍生物损失。以前，Molinet- ribaud通过量规变换建立了$ h^{1}（\ mathbb {t}，\ mathbb {r}）$的本地良好。我们以$ h^{s}（\ Mathbb {t}，\ Mathbb {r}）$，$ s> 1/2 $和本地良好的质量和local-h^{s}（s s s}（\ Mathbb {t}，\ MathBB {r}）$ geq 3中，我们显示了本地存在和先验估计。在四分之一的非线性的情况下，我们证明了以较小的初始数据为条件的全球溶液存在。
New low regularity well-posedness results for the generalized Benjamin-Ono equations with quartic or higher nonlinearity and periodic boundary conditions are shown. We use the short-time Fourier transform restriction method and modified energies to overcome the derivative loss. Previously, Molinet--Ribaud established local well-posedness in $H^{1}(\mathbb{T},\mathbb{R})$ via gauge transforms. We show local existence and a priori estimates in $H^{s}(\mathbb{T},\mathbb{R})$, $s>1/2$, and local well-posedness in $H^{s}(\mathbb{T},\mathbb{R})$, $s\geq3/4$ without using gauge transforms. In case of quartic nonlinearity we prove global existence of solutions conditional upon small initial data.
