In this paper we consider the two component b-family of equations on \({\mathbb {R}}\). We write the equations on a Sobolev type diffeomorphism group. As an application of this formulation we show that the dependence on the initial data is nowhere locally uniformly continuous. In particular it is nowhere locally Lipschitz and nowhere locally Hölder continuous.

中文翻译：

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关于二分量b族方程的局部适定性

在本文中，我们考虑\({\mathbb {R}}\)上的两个分量b方程族。我们在 Sobolev 型微分同胚群上写方程。作为该公式的应用，我们表明对初始数据的依赖在任何地方都不是局部一致连续的。特别是它在局部 Lipschitz 和局部 Hölder 处都不连续。