Navier-Stokes equations
Math equations that describe how liquids and gases move.
The Navier-Stokes equations are a set of mathematical rules that describe the motion of fluids like water and air. They are fundamental to understanding everything from weather patterns to how airplanes fly.
Think about how water flows in a river or how smoke rises from a fire. These equations help scientists and engineers predict and analyze these movements. For example, they can be used to design more efficient cars or to model the spread of pollution.
The Navier-Stokes equations are a system of partial differential equations that describe the motion of viscous fluid substances. They represent the conservation of momentum and mass for a Newtonian fluid. The equations are notoriously difficult to solve analytically, especially in three dimensions, and proving the existence and smoothness of solutions is one of the Clay Mathematics Institute's Millennium Prize Problems.
The Navier-Stokes equations are currently a hot topic due to OpenAI's claim that its AI has solved this 90-year-old mathematical problem. This claim has generated significant debate within the scientific community, raising questions about AI's capabilities in advanced mathematics and the validation of such discoveries.
- OpenAI’s math solutions aren’t meeting the field’s standards yetOpenAI · TechCrunch AI ·
- Why Jensen Huang Believes We’ve Reached AGI and Inside OpenAI’s German Website Hijack | #287OpenAI · Moonshots with Peter Diamandis ·
- What's going on with OpenAI and the Navier-Stokes controversy?OpenAI · Engadget AI ·
- OpenAI says it cracked 90-year-old maths problem in 88 hoursOpenAI · BBC Technology ·
- OpenAI Just Claimed a Huge Math Discovery. Some Academics Are Crying FoulOpenAI · WIRED AI ·
- OpenAI's historic math solution overshadowed by credit controversyOpenAI · Axios AI ·
- On the Navier–Stokes Millennium Prize ProblemOpenAI · OpenAI News ·
- OpenAI ChatGPT
- OpenAI's AI systems have been reportedly used to tackle and potentially solve the Navier-Stokes Millennium Prize problem, a complex challenge in fluid dynamics.
The equations are named after French engineer and physicist Claude-Louis Navier and Russian-born mathematician George Gabriel Stokes. They were developed independently in the early 19th century. Source ↗
You can ask a large language model like ChatGPT or Gemini to explain a specific aspect of fluid dynamics using the Navier-Stokes equations. For instance, ask it to describe how these equations help predict weather patterns or design airplane wings. You can also ask it to provide a simplified analogy for how these equations work.
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Questions people ask
- Are the Navier-Stokes equations easy to solve?
- No, the Navier-Stokes equations are very difficult to solve, especially for complex scenarios. Proving the existence and smoothness of their solutions is a major unsolved problem in mathematics.
- What kind of problems do the Navier-Stokes equations help solve?
- They help solve problems related to the movement of liquids and gases, such as weather forecasting, designing aircraft, understanding blood flow, and predicting ocean currents.
First seen on Subvolts Sep 8, 2026. Updated Oct 15, 2026. Written by an AI model from the items above and reviewed against them weekly; report an error.