A note on the Cauchy problem for $-D_0^2+2x_1D_0D_2+D_1^2+x_1^3D_2^2+\sum_{j=0}^2b_jD_j$

TL;DR

This paper improves the understanding of the non-solvability of a specific second-order differential operator's Cauchy problem in the Gevrey class, lowering the order threshold from 6 to 5.

Contribution

It refines previous non-solvability results by establishing non-solvability at a lower Gevrey order for the operator's Cauchy problem.

Findings

Proves non-solvability at Gevrey order > 5

Reduces the previously known order from 6 to 5

Focuses on a specific second-order differential operator

Abstract

In this note, we improve a previously proven non-solvability result of the Cauchy problem for the Cauchy problem in the Gevrey class for a homogeneous second-order differential operator mentioned in the title. We prove that the Cauchy problem for this operator is not locally solvable at the origin for any lower order term in the Gevrey class of order greater than 5, lowering the previously obtained Gevrey order 6.