标题： 关于ILW方程在$H^s(\mathbb{T})$对于$s>-\frac12$的整体适定性 显示英文标题

标题： Global well-posedness for the ILW equation in $H^s(\mathbb{T})$ for $s>-\frac12$

摘要： 我们证明了中间长波（ILW）方程在Sobolev空间$H^s(\mathbb{T})$中对于$s > -\frac12$是全局适定的。适定性的先前记录为$s\geq 0$，并且已知系统对于$s<-\frac12$是不适定的。然后我们演示了ILW的解在无限深度极限下收敛到Benjamin-Ono方程的解$H^s(\mathbb{T})$。我们的方法并不依赖于ILW的完全可积性，而是将其视为Benjamin-Ono方程受零阶线性项扰动的情况。为了突出这一点，我们建立了关于此类扰动的一个通用适定性结果，该结果也适用于大陆架波的Smith方程。 显示英文摘要

摘要： We prove that the intermediate long wave (ILW) equation is globally well-posed in the Sobolev spaces $H^s(\mathbb{T})$ for $s > -\frac12$. The previous record for well-posedness was $s\geq 0$, and the system is known to be ill-posed for $s<-\frac12$. We then demonstrate that the solutions of ILW converge to those of the Benjamin--Ono equation in $H^s(\mathbb{T})$ in the infinite-depth limit. Our methods do not rely on the complete integrability of ILW, but rather treat ILW as a perturbation of the Benjamin--Ono equation by a linear term of order zero. To highlight this, we establish a general well-posedness result for such perturbations, which also applies to the Smith equation for continental-shelf waves.