论文标题
用于立方schrödinger半波方程的精致概率局部良好的属性
Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation
论文作者
论文摘要
我们获得了具有立方非线性的Schrödinger半波方程的准线性方程式中的概率局部适应性。由于在Picard的迭代中缺乏概率平滑，因此我们需要使用精致的Ansatz，这是由于高低低频率相互作用所致。证明是对在衍生非线性波方程式上将其带到Schrödinger-type方程的方法的适应。此外，我们讨论了该方程式的不良性结果。
We obtain probabilistic local well-posedness in quasilinear regimes for the Schrödinger half-wave equation with a cubic nonlinearity. We need to use a refined ansatz because of the lack of probabilistic smoothing in the Picard's iterations, which is due to the high-low-low frequency interactions. The proof is an adaptation of the method of Bringmann on the derivative nonlinear wave equation to Schrödinger-type equations. In addition, we discuss ill-posedness results for this equation.
