论文标题
严格凸域和应用程序中的schr {Ö} dinger方程的分散估计值
Dispersive estimates for the Schr{ö}dinger equation in a strictly convex domain and applications
论文作者
论文摘要
我们考虑了一个尺寸的严格凸域$ d \ geq 2 $的各向异性模型案例，并描述了具有Dirichlet边界条件的半古典schr {Ö} dinger方程的分散。更具体地说，我们获得了线性半经典流量的以下固定时间衰减率：$（\ frac ht）^{1/4} $的损失是由于重复的燕尾型奇异性而导致的边界较小的情况，并且被证明是最佳的。 相应的Strichartz估计值允许在此类3D模型凸域上求解立方非线性Schödinger方程，因此可以在通用紧凑的无边界歧管上匹配已知结果。
We consider an anisotropic model case for a strictly convex domain of dimension $d\geq 2$ with smoothboundary and we describe dispersion forthe semi-classical Schr{ö}dinger equation with Dirichlet boundary condition. More specifically, we obtain the following fixed time decay rate for the linear semi-classical flow : a loss of $(\frac ht)^{1/4}$ occurs with respect to the boundary less case due to repeated swallowtail type singularities, and is proven optimal. Corresponding Strichartz estimates allow to solve the cubic nonlinear Schödinger equation on such a 3D model convex domain, hence matching known results on generic compact boundaryless manifolds.
