We study the local well-posedness for higher order Benjamin-Ono type equations, especially fourth order equations. The proof is based on the energy methods with correction terms. Although one of correction terms can eliminate the highest order derivative loss in the energy inequality, it may yield a lower order derivative loss than the worst term. In order to cancel all of the derivative losses, we define correction terms inductively.

中文翻译：

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四阶本杰明-奥诺型方程的局部适定性

我们研究了高阶本杰明-奥诺型方程，特别是四阶方程的局部适定性。该证明基于带有校正项的能量方法。尽管校正项之一可以消除能量不等式中的最高阶导数损失，但与最差项相比，它可能会产生较低阶的导数损失。为了消除所有微分损失，我们归纳定义了校正项。