Abstract
We prove a sharp bilinear inequality for the Klein--Gordon equation on $\mathbb{R}^{d+1}$, for any $d \geq 2$. This extends work of Ozawa--Rogers and Quilodrán for the Klein--Gordon equation and generalizes work of Bez--Rogers for the wave equation. As a consequence, we obtain a sharp Strichartz estimate for the solution of the Klein--Gordon equation in five spatial dimensions for data belonging to $H^1$. We show that maximizers for this estimate do not exist and that any maximizing sequence of initial data concentrates at spatial infinity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.