# The Cauchy problem for operator-Boussinesq equations

## TL;DR

This paper establishes the existence and uniqueness of solutions for the abstract Boussinesq equation's Cauchy problem and extends the results to systems of Boussinesq equations of various orders.

## Contribution

It provides new theoretical results on the well-posedness of the Cauchy problem for abstract and system Boussinesq equations.

## Key findings

- Existence and uniqueness of solutions for the abstract Boussinesq equation.
- Extension of results to finite and infinite order Boussinesq systems.
- Framework applicable to a broad class of Boussinesq-type equations.

## Abstract

In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equation is obtained. By applying this result, the Cauchy problem for systems of Boussinesq equations of finite or infinite orders are studied