Is the Navier-Stokes Conjecture Finally Solved?

In summary, the conversation discusses Penny Smith's proposed proof of smooth solutions for the N-S equations, which could potentially earn her a Clay Millennium Prize and a Fields medal. However, there are concerns about a possible mistake in her proof.
  • #1
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I am surprised that nobody has posted yet of the hottest hews in PDE's, Penny Smith's proposed proof that smooth, "immortal" solutions of the N-S equations exist. If it pans out, this will collect one of the famous Clay Millennium Prizes, a cool million. Smith says that unlike Perelman, she'd take it. She would also be a shoo-in for one of the Fields medals to be given four years from now.

See Woit, and especially this
comment by Brooks Moses to the Woit post.
 
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  • #3
  • #4
No. As a Mentor, shouldn't you be able to merge the two? As I said in that thread, I chose the most general category applicable. If you feel that it best suits the DE forum, then please do merge it with this one. :)
 
  • #5
She retracted it after finding a mistake.
 
  • #6
mtiano said:
She retracted it after finding a mistake.

Let's hope that, as she implies on her website, it's not a killer.
 

Related to Is the Navier-Stokes Conjecture Finally Solved?

1. What is the Navier-Stokes equation and why is it important?

The Navier-Stokes equation is a set of partial differential equations that describe the motion of fluid substances. It is important because it is used to model and predict the behavior of fluids in a wide range of applications, such as weather forecasting, aerodynamics, and oceanography.

2. What does it mean for the Navier-Stokes equation to be "cracked"?

To say that the Navier-Stokes equation is "cracked" refers to the fact that it has not yet been proven to have a unique solution for all possible initial conditions. This is known as the Navier-Stokes existence and smoothness problem, which remains one of the most challenging unsolved problems in mathematics.

3. How does the Navier-Stokes equation relate to turbulence?

The Navier-Stokes equation is used to model fluid flow, including turbulent flow. However, due to its complexity, the equation has limitations in accurately predicting turbulent behavior. As a result, there are various turbulence models and theories that have been developed to improve the understanding and prediction of turbulence.

4. What are some potential applications of solving the Navier-Stokes equation?

If the Navier-Stokes existence and smoothness problem were to be solved, it would have significant implications in various fields where fluid dynamics plays a crucial role. This could include more accurate weather forecasting, more efficient design of aircraft and vehicles, and better understanding and management of ocean currents.

5. How are scientists currently tackling the Navier-Stokes existence and smoothness problem?

There are various approaches being taken to try and solve the Navier-Stokes problem, including analytical, computational, and experimental methods. Some researchers are also using high-performance computing to simulate and analyze fluid behavior in order to gain insight into the problem. Collaboration and interdisciplinary efforts are also being pursued to tackle this complex problem.

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