论文标题
2D模型凸域上波方程的Strichartz估计
Strichartz estimates for the wave equation on a 2d model convex domain
论文作者
论文摘要
我们证明，比我们早期在2D凸模型上获得的（最佳）色散的（最佳）分散体所预期的估计值更好。这是从我们获得的参数中充分利用了苛性物的时空定位，尽管它们的数量像从源到边界的距离的反平方根一样增加。结果，我们改善了波动方程的已知strichartz估计值。我们以前的参数构建的几种改进是在途中获得的，并且对进一步的应用具有独立的兴趣。
We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix we obtain, despite their number increasing like the inverse square root of the distance from the source to the boundary. As a consequence, we improve known Strichartz estimates for the wave equation. Several improvements on our previous parametrix construction are obtained along the way and are of independent interest for further applications.
