Elena Cordero, Davide Zucco
Published 2010-05-10, updated 2011-05-19Version 3
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.
Comments: 18 pages, 4 figures, some misprints corrected
Some new Strichartz estimates for the Schrödinger equation
Strichartz Estimates for the Schroedinger Equation with Time-Periodic L^{n/2} Potentials
Randomization improved Strichartz estimates and global well-posedness for supercritical data
![QR code for arXiv:1005.1484 [math.AP]](http://oss.arxitics.com/images/favicon.svg)