But, why is this the hardest problem in Maths & Physics? (#SoME4)

*At around 17:50, the arrow besides lambda should be an up arrow (instead of down arrow). The tilde u_lambda should increase as lambda increases (it's a super-critical quantity). The Navier-Stokes equation is a fundamental concept in fluid dynamics, describing the motion of fluids and the forces that act upon them. This equation is crucial for understanding various phenomena in physics and engineering, including ocean currents, weather patterns, and the flow of fluids in pipelines. In this video, we will delve into the world of fluid dynamics and explore the Navier-Stokes equation in detail, discussing its derivation, applications, and significance in modern science and technology. Whether you're a student of physics, an engineer, or simply someone fascinated by the behavior of fluids, this video aims to provide a comprehensive introduction to the Navier-Stokes equation and its importance in understanding the world around us. By the end of this video, you will have a deeper understanding of this complex equation and its role in shaping our understanding of fluid motion. But, why are the Navier-Stokes equations so hard and difficult to solve? why does this happen? You and I are gonna explore one of the three strategies proposed by Terence Tao as a possible path to tackle such a problem. Resources: 1. CMI Official Statement: https://www.claymath.org/millennium/n... 2. Terence Tao's Proposed Strategies: https://terrytao.wordpress.com/2007/0... 3. Olga Ladyzhenskaya's Inequality: https://en.wikipedia.org/wiki/Ladyzhe... YouTube Videos that helped me: 1. Navier Stokes Equation by Aleph 0:    • Navier Stokes Equation | A Million-Dollar ...   2. Navier-Stokes Equations by Numberphile (Tom Crawford):    • Navier-Stokes Equations - Numberphile   3. The million dollar equation by vcubingx:    • The million dollar equation (Navier-Stokes...   ▶️ A $1M dollar podcast clip that motivated me:    • $1 million dollar unsolved math problem: N...   Chapters: 00:00 What are Navier-Stokes Equations? 00:41 What it means to find a solution of a PDE? 01:44 The Million-Dollar Problem 02:14 Strategies proposed by Terence Tao 02:43 Describing Navier-Stokes Equations & Assumptions 06:05 Simplifying Navier-Stokes Equation 07:27 1D Navier-Stokes Equation 07:58 The partial differentitation 08:46 The Good Term -- Diffusion 10:31 The Bad Term -- Advection 11:29 Who wins the Duel? 12:05 Scaling the Navier-Stokes Equation 15:00 Lp Norm of a function 17:10 Combining everything we know 19:49 Can you win a million dollar prize? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This video is animated using Manim library (based on Python). Manim is an engine for precise programmatic animations, designed for creating explanatory math videos. Code for this video: https://github.com/Varniex/animations Let's connect: Instagram:   / varniex.vx   Twitter:   / varniex   ManimGL GitHub Repository: https://github.com/3b1b/manim Support the Channel: Become a Patreon:   / varniex   Buy me a Book: https://buymeacoffee.com/Varniex ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #some4 #physics #maths