论文标题
Schroedinger动力学的散射波运算符的L^P有界性，该动力学具有时间相关电位和应用
L^p Boundedness of the Scattering Wave Operators of Schroedinger Dynamics with Time-dependent Potentials and applications
论文作者
论文摘要
本文在$ \ mathbb {r}^3 $中建立了Wave Operator的$ l^p $界限，并具有时间相关的电位。证明的方法基于新的取消引理。作为基于此方法的典型应用，与Strichartz估计的结合是非线性分散方程的存在和散射。例如，我们在$ l^{\ infty} $中证明了全球存在和统一的界限，对于$ l^2中的Hartreenonlinearschrödinger方程（\ Mathbb {r}^3），$允许solitons的存在。我们还证明了$ p> p_c（n）$中的$ l^p（\ mathbb {r}^n）$中的自由通道波运算符，带有$ p_c（3）= 6 $。
This paper establishes the $L^p$ boundedness of wave operators for linear Schrödinger equations in $\mathbb{R}^3$ with time-dependent potentials. The approach to the proof is based on new cancellation lemmas. As a typical application based on this method, combined with Strichartz estimates is the existence and scattering for nonlinear dispersive equations. For example, we prove global existence and uniform boundedness in $L^{\infty}$, for a class of Hartree nonlinear Schrödinger equations in $L^2(\mathbb{R}^3),$ allowing the presence of solitons. We also prove the existence of free channel wave operators in $L^p(\mathbb{R}^n)$ for $p>p_c(n)$, with $p_c(3)=6$.
