Strichartz Estimates for the Vibrating Plate Equation
Analysis of PDEs
2011-05-20 v3 Mathematical Physics
math.MP
Abstract
We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.
Keywords
Cite
@article{arxiv.1005.1484,
title = {Strichartz Estimates for the Vibrating Plate Equation},
author = {Elena Cordero and Davide Zucco},
journal= {arXiv preprint arXiv:1005.1484},
year = {2011}
}
Comments
18 pages, 4 figures, some misprints corrected