论文标题
具有孤立奇点的非线性schrödinger方程的良好姿势
Well posedness of the nonlinear Schrödinger equation with isolated singularities
论文作者
论文摘要
我们研究非线性schrödinger（NLS）方程的良好姿势，在二和三维中具有点相互作用和功率非线性。这是该问题的自主兴趣的背后，这是所谓奇异溶液演变的模型，这些模型在半线性椭圆方程分析中众所周知。我们表明，NLS认为的库奇问题享有强（操作员域）解决方案的局部存在和独特性，并且该解决方案不断取决于初始数据。在维度中，两个良好的姿势对任何权力的非线性都具有，并且全球存在被证明是下方的权力。在维度中，三个本地和全球良好的姿势仅限于低力量。
We study the well posedness of the nonlinear Schrödinger (NLS) equation with a point interaction and power nonlinearity in dimension two and three. Behind the autonomous interest of the problem, this is a model of the evolution of so called singular solutions that are well known in the analysis of semilinear elliptic equations. We show that the Cauchy problem for the NLS considered enjoys local existence and uniqueness of strong (operator domain) solutions, and that the solutions depend continuously from initial data. In dimension two well posedness holds for any power nonlinearity and global existence is proved for powers below the cubic. In dimension three local and global well posedness are restricted to low powers.
