论文标题
$ e^s_σ$中非本地（衍生）NLS的全局cauchy问题
Global Cauchy problems for the nonlocal (derivative) NLS in $E^s_σ$
论文作者
论文摘要
我们考虑了超临界功能空间中（衍生）非局部NLS的库奇问题$ e^s_σ$，该规范由$ \ | f \ | __ {e^s_σ} =定义。 。 $$任何sobolev space $ h^{r} $是$ e^s_σ$的子空间，即，$ h^r \ subset e subset e^s_σ$ for noity $ r，σ\ in \ mathbb {r} $和$ s <0 $。对于非本地NLS（对于非局部衍生NLS），令$ s <0 $和$σ> -1/2 $（$σ> 0 $）。如果最初的数据属于$ e^s_σ$，则我们显示了解决方案的全局存在和独特性，并且其傅立叶变换在$（0，\ infty）$中支持，那么全球解决方案不需要$ e^s_σ$的初始数据的较小条件。
We consider the Cauchy problem for the (derivative) nonlocal NLS in super-critical function spaces $E^s_σ$ for which the norms are defined by $$ \|f\|_{E^s_σ} = \|\langleξ\rangle^σ2^{s|ξ|}\hat{f}(ξ)\|_{L^2}, \ s<0, \ σ\in \mathbb{R}. $$ Any Sobolev space $H^{r}$ is a subspace of $E^s_σ$, i.e., $H^r \subset E^s_σ$ for any $ r,σ\in \mathbb{R}$ and $s<0$. Let $s<0$ and $σ>-1/2$ ($σ>0$) for the nonlocal NLS (for the nonlocal derivative NLS). We show the global existence and uniqueness of the solutions if the initial data belong to $E^s_σ$ and their Fourier transforms are supported in $(0, \infty)$, the smallness conditions on the initial data in $E^s_σ$ are not required for the global solutions.
