# Analysis of solutions for a cerebrospinal fluid model

## TL;DR

This paper investigates a mathematical model of cerebrospinal fluid dynamics, establishing existence and uniqueness of solutions and validating findings through numerical simulations under various initial conditions.

## Contribution

It provides a rigorous mathematical analysis of the cerebrospinal fluid model, including proofs of solution existence, uniqueness, and numerical validation.

## Key findings

- Existence and uniqueness of local solutions proven.
- Global solutions exist under certain initial data restrictions.
- Numerical simulations confirm theoretical results.

## Abstract

The main purpose of this manuscript is to analyze an intracranic fluid model from a mathematical point of view. By means of an iterative process we are able to prove the existence and uniqueness of a local solution and the existence and uniqueness of a global solution under some restriction conditions on the initial data. Moreover the last part of the paper is devoted to present numerical simulations for the analyzed cerebrospinal model. In particular, in order to assess the reliability of the stated theoretical results, we carry out the numerical simulations in two different cases: first, we fix initial data which satisfy the conditions for the global existence of solution then, we choose initial data that violate them.