Well-posedness of NLS on $R×S^3$
A talk in the Oberseminar Analysis series by
Yunfeng Zhang
| Abstract: | We show that the cubic NLS on the four-dimensional product manifold $R×S^3$ is globally well-posed for small initial data in the critical space, namely the energy space. There are two key ingredients for the proof. Firstly, via representation theory, we prove the sharp bilinear eigenfunction estimate on the three-sphere $S^3$, eliminating the logarithmic loss in the pioneering work of Burq, Gérard, and Tzvetkov. Secondly, we establish a refined mixed-norm type Strichartz estimate on the cylindrical space $R×T$, by a combination of measure estimates and a novel kernel decomposition. Zoom ID: [639 2876 8344] Passcode: [054853] Within the CRC this talk is associated to the project(s): A1 |