论文标题
时间分级的schrödinger操作员的平滑效果
Smoothing effect for time-degenerate Schrödinger operators
论文作者
论文摘要
在这项工作中，我们考虑了线性时间分级施罗丁操作员的示例。我们表明，使用适当的假设，操作员满足了Kato平滑效果。我们还表明，涉及该运算符和多项式衍生品非线性的非线性初始值问题的解决方案是局部供应良好的，并且它们的溶液也满足与线性溶液相同的平滑估计值。
In this work we consider an example of a linear time-degenerate Schrödinger operator. We show that with the appropriate assumptions the operator satisfies a Kato smoothing effect. We also show that the solutions to the nonlinear initial value problems involving this operator and polynomial derivative nonlinearities are locally well-posed and their solutions also satisfy the same smoothing estimates as the linear solutions.
