# Gevrey estimates for certain moment partial differential equations

## TL;DR

This paper establishes Gevrey estimates for formal solutions of inhomogeneous linear moment differential equations with holomorphic time-dependent coefficients, advancing the understanding of their regularity and growth properties.

## Contribution

It introduces a method combining formal norms, majorant theory, and Newton polygon analysis to derive Gevrey estimates for these equations.

## Key findings

- Gevrey estimates are obtained for formal solutions.
- The approach uses formal norms and majorant theory.
- Newton polygon properties are key to the analysis.

## Abstract

We consider the Cauchy problem for inhomogeneous linear moment differential equations with holomorphic time dependent coefficients. Using such tools as the formal norms, theory of majorants and the properties of the Newton polygon, we obtain the Gevrey estimate for the formal solution of the equation.