A Student's Guide to the Navier-Stokes Equations

The Navier-Stokes equations describe the motion of fluids and are an invaluable addition to the toolbox of every physicist, applied mathematician, and engineer. The equations arise from applying Newton's laws of motion to a moving fluid and are considered, when used in combination with mass and energy conservation rules, to be the fundamental governing equations of fluid motion. They are relevant across many disciplines, from astrophysics and oceanic sciences to aerospace engineering and materials science. This Student's Guide provides a clear and focused presentation of the derivation, significance and applications of the Navier-Stokes equations, along with the associated continuity and energy equations. Designed as a useful supplementary resource for undergraduate and graduate students, each chapter concludes with a selection of exercises intended to reinforce and extend important concepts. Video podcasts demonstrating the solutions in full are provided online, along with written solutions and other additional resources.

Navier-Stokes方程式描述了流體的運動，對於每位物理學家、應用數學家和工程師來說，它們是一個非常寶貴的工具。這些方程式是從將牛頓運動定律應用於流動流體中而得出的，當與質量和能量守恆規則結合使用時，被認為是流體運動的基本控制方程式。它們在許多學科中都具有相關性，從天體物理學和海洋科學到航空航天工程和材料科學。本學生指南清晰而重點突出地介紹了Navier-Stokes方程式的推導、重要性和應用，以及相關的連續性和能量方程式。作為本科和研究生學生的有用補充資源，每章結束時都附有一些旨在加強和擴展重要概念的練習題。在線提供了展示完整解答的視頻播客，以及書面解答和其他附加資源。