The Cauchy Problem for the Vibrating Plate Equation in modulation spaces

TL;DR

This paper investigates the local solvability of the nonlinear vibrating plate equation within modulation spaces and demonstrates the lack of well-posedness in Wiener amalgam spaces, highlighting the importance of the functional framework.

Contribution

It establishes local solvability results in modulation spaces and shows ill-posedness in Wiener amalgam spaces for the vibrating plate equation.

Findings

Local solvability in modulation spaces

Ill-posedness in Wiener amalgam spaces

Differentiates functional frameworks for well-posedness

Abstract

The local solvability of the Cauchy problem for the nonlinear vibrating plate equation is showed in the framework of modulation spaces. In the opposite direction, it is proved that there is no local wellposedness in Wiener amalgam spaces even for the solution to the homogeneous vibrating plate equation.