# Solving and Visualizing Navier–Stokes Equations in the Cloud-9/12

> The Navier–Stokes equations are crucial because they provide a comprehensive framework to understand and predict fluid motion across many disciplines, from designing vehicles and power stations to studying environmental flows and biological systems, while also representing a deep mathematical challenge

[Leveraging cloud computing resources is essential for efficiently simulating and visualizing complex fluid dynamics phenomena](https://viadean.notion.site/Solving-and-Visualizing-Navier-Stokes-Equations-in-the-Cloud-2D-Steady-Stokes-Flow-9-12-21f1ae7b9a3280828cb5c170a2cbc0bb?source=copy_link), specifically focusing on the computational demands of solving the Navier-Stokes equations for applications like animating particle traces in 2D steady Stokes flow.

### :clapper:Animated result

{% embed url="<https://youtu.be/TfOxlnzXTv0>" %}
particle traces in a 2D steady Stokes flow
{% endembed %}