论文标题
在两个空间维度中的中临界对数修饰的非线性schrodinger方程式上
On an intercritical log-modified nonlinear Schrodinger equation in two spatial dimensions
论文作者
论文摘要
我们考虑通过对数因子比立方体大的schr {Ö} dinger类型的分散方程。该方程式被认为是具有Lhy校正的稳定二维量子液滴的有效模型。从数学上讲，它被认为是质量超临界和能量亚临界，具有标志性非线性。对于相应的初始值问题，我们证明了能量空间中强溶液的全球时间存在。此外，我们证明了非线性接地态的存在和独特性（最多与对称性）以及一组能量最小化器的轨道稳定性。我们还表明，对于1D中的相应模型，可获得更强的稳定性结果。
We consider a dispersive equation of Schr{ö}dinger type with a non-linearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model for stable two dimensional quantum droplets with LHY correction. Mathematically, it is seen to be mass supercritical and energy subcritical with a sign-indefinite nonlinearity. For the corresponding initial value problem, we prove global in-time existence of strong solutions in the energy space. Furthermore, we prove the existence and uniqueness (up to symmetries) of nonlinear ground states and the orbital stability of the set of energy minimizers. We also show that for the corresponding model in 1D a stronger stability result is available.
