We consider the Benjamin–Ono equation on the real line for initial data in weighted Sobolev spaces. After the application of the gauge transform, the flow is shown to be Lipschitz continuous and to present a nonlinear smoothing effect. As a consequence, unconditional uniqueness for the Benjamin–Ono equation is proved.

中文翻译：

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加权Sobolev空间中Benjamin-Ono方程的非线性平滑和无条件唯一性

对于加权Sobolev空间中的初始数据，我们考虑实线上的Benjamin-Ono方程。应用轨距变换后，流场显示为Lipschitz连续流，并呈现非线性平滑效果。结果，证明了本杰明-奥诺方程的无条件唯一性。