# $C^{1,\theta}$-Estimates on the distance of Inertial Manifolds

## TL;DR

This paper establishes $C^{1, heta}$-estimates for the distance between inertial manifolds of parabolic systems in different phase spaces, linking the estimates to resolvent operators and nonlinearities.

## Contribution

It provides new $C^{1, heta}$-estimates for inertial manifold distances considering systems in different phase spaces, a novel extension in the field.

## Key findings

- Derived $C^{1, heta}$-estimates for inertial manifold distances.
- Linked the estimates to resolvent operators and nonlinearities.
- Applicable to systems with different phase spaces.

## Abstract

In this paper we obtain $C^{1,\theta}$-estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we estimate the distance in terms of the distance of the resolvent operators of the corresponding elliptic operators and the distance of the nonlinearities of the equations.