Analysis of solutions for a cerebrospinal fluid model

The aim of this manuscript is to analyze an intracranial fluid model from a mathematical point of view. The novel aspect of this work with respect to the existing literature is represented by the rigorous mathematical results regarding the analysis of the solutions to the systems of equations which model the different mechanisms in the cerebrospinal fluid compartments. 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 numerical simulations for the analyzed cerebrospinal fluid 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 solutions, then, we choose initial data that violate them.