论文标题
Z和R上的非线性Schrodinger方程，具有有限的初始数据：示例和猜想
The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures
论文作者
论文摘要
我们研究了具有有界的初始数据的非线性Schrödinger方程（NLS），这些数据在无穷大时不会消失。示例包括定期，准周期和随机初始数据。在晶格上，我们证明，对于任何有限的数据，解决方案在多个方面都是多项式界限的。在连续性中，牛顿迭代方案证明了实际分析数据的局部存在。具有正则非线性的NLS的全球存在是通过分析局部能量规范的。
We study the nonlinear Schrödinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove that solutions are polynomially bounded in time for any bounded data. In the continuum, local existence is proved for real analytic data by a Newton iteration scheme. Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm.
