The Burgers equations as a first step towards the study of the incompressible flows (Lecture notes, in spanish)

TL;DR

This paper introduces the Burgers equations as a foundational step towards understanding incompressible fluid flows, covering mathematical proofs and numerical methods, aimed at students and researchers in fluid dynamics.

Contribution

It provides a comprehensive presentation of the Burgers equations, including existence and uniqueness proofs and practical numerical techniques, as an educational resource.

Findings

Proof of existence and uniqueness for Burgers equation

Introduction of numerical methods for solving Burgers equations

Educational material for incompressible fluid dynamics

Abstract

In this lecture notes we present the equations and the physics involved in the dynamic of incompressible fluids. We present the mathematical techniques needed in order to prove the existence and uniqueness result for the case where we consider Burgers equation. We also explain an useful numerical method when dealing with this kind of equations. These lecture notes were written for the 2010 JAE-Intro Summer School. This Summer School was organized by ICMAT-CSIC and takes place in Madrid.