The purpose of this paper is to investigate the well-posedness in the (weighted) energy space of a Schrödinger–Poisson model with additional chiral nonlinearity proportional to the electric current ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4837/nonab8fb4ieqn1.gif] {$j\left[\psi \right]=\mathrm{I}\mathrm{m}\left(\overline{\psi }{\psi }_{x}\right)$} . More precisely, a unique mild solution of the nonlinear initial value problem ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4837/nonab8fb4ieqn2.gif] {$i{\psi }_{t}+{\psi }_{xx}=\frac{1}{2}\left(\vert x\vert {\ast}\vert \psi {\vert }^{2}\right)\psi -\lambda j\left[\psi \right]\psi \;,\quad \psi \left(0,x\right)={\psi }_{0}\left(x\right),$} is shown to exist globally in ##IMG## [http://ej.iop.org/im...] {${X}_{1}\left(\mathbb{R}\right)=\left\{\phi \in {H}^{1}\left(\mathbb{R}\right):{\left(1+{x}^{2}\right)}^{\frac{1}{4}}\phi \in {L}^{2}\left(\mathbb{R}\right)\right\}$}

中文翻译：

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描述非线性手性效应的Schrödinger-Poisson模型的适定性

本文的目的是研究在Schrödinger-Poisson模型的（加权）能量空间中的适定性，以及与电流## IMG ##成比例的其他手性非线性[http://ej.iop.org/ images / 0951-7715 / 33/9/4837 / nonab8fb4ieqn1.gif] {$ j \ left [\ psi \ right] = \ mathrm {I} \ mathrm {m} \ left（\ overline {\ psi} {\ psi } _ {x} \ right）$}。更准确地说，是非线性初始值问题的唯一温和解## IMG ## [http://ej.iop.org/images/0951-7715/33/9/4837/nonab8fb4ieqn2.gif] {$ i {\ psi} _ {t} + {\ psi} _ {xx} = \ frac {1} {2} \ left（\ vert x \ vert {\ ast} \ vert \ psi {\ vert} ^ {2} \ right ）\ psi-\ lambda j \ left [\ psi \ right] \ psi \;，\ quad \ psi \ left（0，x \ right）= {\ psi} _ {0} \ left（x \ right）， $}显示为在## IMG ##中全局存在[http：//ej.iop.org/im ...] {$ {X} _ {1} \ left（\ mathbb {R} \ right）= \ left \ {\ phi \ in {H} ^ {1} \ left（\ mathbb {R} \ right）：