Chapter 140 The successful solution will bring human civilization to a new level
During the millennium, the Clay Mathematics Institute in Amherstia issued a bounty order for seven millennium mathematical problems. Anyone who solves any of these problems can receive a reward of US$1 million.
The seven difficult problems are: NPC complete problem, Hodge conjecture, Poincaré conjecture, Riemann conjecture, Yang-Mills existence and mass gap, Navier-Stokes equation, and Behe-Swedenton-Dyer conjecture.
It is worth mentioning that of these seven major problems, only six are now left.
The Poincaré conjecture was solved by the Chinese mathematician Grigory Perelman in 2002-2003.
Meng Qiuyan stood aside and watched thoughtfully and said: "The most difficult thing to quantify about fluids is the uncontrollability at the micro level. It is simply impossible to analyze the movement of each microscopic particle from the microscopic level." Variables, and these invariants always obey certain conservation laws. "
"No matter how many microscopic particles there are in the fluid, it can always be described by four physical quantities: pressure, temperature, speed and density."
"Look for change in the constant, find the invariant in the change, and find the invariant first when you are in doubt. This invariant is the conserved quantity. There are conserved quantities in everything, and the same is true for fluids."
Strictly speaking, invariants and conserved quantities are not the same thing. They are two different physical concepts.
At the end, Meng Qiuyan let out a long breath. She looked at the content on the whiteboard again and said doubtfully: "These don't look like they are meant to solve the Navier-Stokes equations. Could it be that I'm too stupid..."
Lu An turned around and glanced at the woman. Friend, said: "It is true that it is not the solution to the Navier-Stokes equation, but it is also true that the existing mathematical system cannot solve this equation, so new theoretical tools must be created to solve it."
As soon as these words came out, Meng Qiuyan was stunned on the spot. Only he dared to say such things.
Lu An withdrew his gaze and continued with his business.
After a long time, she came to her senses, shook her head and said to herself: "Forget it, being confused is hard on the brain, I'm still responsible for worshiping, being confused is not hurting the brain."
But after a while, Meng Qiuyan couldn't help but said: "By the way, can you really solve the Navier-Stokes equation?"
Lu An said without looking back: "Yes."
Hearing what he said, Meng Qiuyan blinked her eyes and said, "If we can really find an analytical solution to the Navier-Stokes equation, human civilization will probably reach a new level."
Although Meng Qiuyan couldn't understand it, she also knew that solving the "existence and smoothness" problem of the Navier-Stokes equation would be a revolutionary breakthrough in the fields of mathematics and applied science, and its impact would far exceed fluid mechanics itself.
In the field of mathematics, it can promote a leap in the theory of nonlinear partial differential equations. The Navier-Stokes equation is a typical nonlinear coupled partial differential equation, and the nature of its solution is the core problem of modern analysis.
Solving this problem requires the creation of new mathematical tools, and these tools are extended to the study of other nonlinear equations, such as Einstein's field equations, quantum mechanical equations, etc., which can greatly change human understanding of the mathematical description of complex systems.
In the fields of physics and engineering, being able to move from "empirical science" to "theoretical precision" is the biggest reason why Lu An spends time solving the Navier-Stokes equations. He wants to solve real real problems.
At present, prediction of fluid flow in engineering relies on numerical simulation, such as aircraft aerodynamic design, weather forecast, oil and gas pipeline transportation, etc.
However, the reliability of numerical methods is based on two implicit assumptions: the solution is smooth within the simulation time, otherwise the numerical results will be distorted; secondly, even if turbulence exists, its complex but limited scale can still be captured by the grid.
If it is proven that there is a globally smooth solution to the three-dimensional Navier-Stokes equation, the reliability of the numerical simulation will be theoretically verified. As long as the grid is fine enough, the flow can be accurately described without worrying about the unpredictability caused by singularities.
This breakthrough will allow the design in the aerospace, energy, and shipbuilding fields to shift from "experience trial and error" to "theory-driven".
Speaking human language means that the efficiency is greatly improved and the cost is greatly reduced.
For example, accurately predict drag and lift to design more energy-efficient aircraft; accurately simulate turbulent mixing to optimize engine combustion efficiency; more reliably simulate the evolution of atmospheric vortices to improve weather forecast accuracy.
It is not only the fields of physics and engineering that can usher in revolutionary breakthroughs.
In the field of climate and environment, it has more accurate simulations of ocean circulation and atmospheric motion, improving the ability to predict global warming and extreme weather.
In the field of biomedicine, accurate simulation of the flow of blood in blood vessels and the movement of airflow in the lungs promotes disease treatment and medical device design.
In the energy field, optimize the shape of wind turbine blades, such as utilizing turbulence energy, improving nuclear reactor cooling systems, and avoiding local high temperatures.
In summary, the Navier-Stokes equations are a bridge between pure mathematics and applied science.
Solving this problem will reshape human beings' ability to control fluid motion, profoundly change many fields such as aerospace, energy, climate, and biology from theory to practice, and may even give rise to a new technological revolution.
Not only does the solution to the Navier-Stokes equations already exist in Lu An's mind, he also knows how to solve the other five Millennium problems.
Because, the truth is in his brain.
This is all because Lu An encountered the cosmic disaster of vacuum decay in his previous life. His consciousness miraculously survived in some unknown state after the vacuum decay, and he gained insight into the truth during that strange state. A series of problems that had troubled him for hundreds of years were suddenly revealed.
"If you solve the Navier-Stokes equation problem, you will probably win both the Fields Medal and the Nobel Prize in Physics." Meng Qiuyan lowered her eyes and thought for a moment. She raised her eyes and looked at Lu An, raised the corner of her mouth, and said with a smile: "Oh~, there is also a reward from the Clay Mathematics Institute, which is a full US$1 million. This should be the hardest US$1 million in the world to earn."
Lu An glanced at his girlfriend and said in a relaxed tone: "The value of the analytical solution to the Navier-Stokes equation is more than 1 million U.S. dollars. Even 100 trillion U.S. dollars is not much. It is equivalent to a doubling accelerator that promotes the development of human science and technology. It will usher in a wave of technological explosion in the short term. Its value is difficult to quantify with specific numbers."
Meng Qiuyan asked curiously: "After you solve it, when do you plan to publish a paper?"
Hearing this, Lu An immediately smiled: "Publish a paper? You can't just publish it casually. You have to communicate with the country in advance and get approval. If you don't approve it, you can't publish it."
If Lu An publishes it quietly, it becomes an established fact, and the country can only recognize it.
Then he sent someone over to complain a few words. He didn’t even say hello for such a big matter. If anything similar happens in the future, he must report it in advance.
Lu An said: "The Navier-Stokes equation involves many fields of applied science and will bring huge technological progress. It is only the development of military equipment, such as aircraft and fighter jets, as well as the aerospace field, etc., which involves national defense and high-precision fields."
The current research and development ideas of scientific and technological personnel mainly rely on "experience induction" and "accumulation of trial and error", and continuous trial and error. This is cost-effective and slow, but because the theory is not accurate, it can only be verified through trial and error accumulation until the correct answer is found.
The solution to the Navier-Stokes equations, from empirical simulation to theoretical accuracy, essentially makes "theoretical predictions" more reliable, thereby reducing the cost of trial and error.
For example, when the theoretical accuracy is 70%, it takes 1,000 trials and errors to find the answer.
The solution of the Navier-Stokes equation suddenly increased the theoretical accuracy to more than 99.999%. What originally required 1,000 trials and errors may only take 10 or even once to find the answer.
This will undoubtedly greatly reduce trial and error costs and time costs, and the efficiency will also increase significantly.
After solving the Navier-Stokes equation, the current role of actual verification can be transformed from the original "leader" and "sole basis" to the theoretical "calibrator" and "boundary detector".
When you are still using the trial-and-error-led logic of traditional empirical science to develop a new fighter jet or new rocket, it will take ten to twenty years and tens of billions or even hundreds of billions of funds invested.
But I figured out the Navier-Stokes equation and did the same thing. The time period changed from "years" to "months". I could realize a new rocket from project establishment to first flight in just ten months, and the funds invested also dropped sharply.
You waste money, time and effort, I save money, time and effort.
The advantages of this are self-evident.
Meng Qiuyan thought about it and couldn't help but nodded and said: "If it's purely theoretical and mathematical, it's okay to publish it publicly, but if it involves applied science and the results can be quickly transformed, it's really not appropriate to publish them publicly."
At this time, Lu An thought briefly and suddenly said: "It still has to be published."
Meng Qiuyan: "???"
Lu An looked at each other and smiled and said: "Publish it, but make it difficult for them to understand. I incorporated some other factors into the paper to make the verification cost skyrocketing, making it impossible for outsiders to prove or falsify."
Meng Qiuyan was confused: "Isn't this unnecessary?"
Lu An shook his head and said: "This is very necessary. I solved the Navier-Stokes equation not to just put it on the shelf to admire myself, but to transform it into applications. When it reaches the application stage, it will definitely not be concealed. It can be easily inferred that I have solved this equation." If you don't put it down, it will appear to be out of order and a bit ignorant. "
At this point, Lu An looked at Meng Qiuyan, who was thoughtful, and added with a smile: "So, I published the paper, but no one in the world can understand it, so you can't blame me?"
Meng Qiuyan couldn't help but nodded, and she also knew that Lu An's move was more of a self-protection strategy.
When only Lu An in the world can understand, he has irreplaceable attributes and everyone depends on him. Then nothing can happen to him, which can very well deter the coveters lurking in the dark.
Even if someone wants to forcefully pick the peach, there will be more people siding with Lu An to isolate the coveted person, or even work together to destroy the other party.
As the scale of the business becomes larger and larger in the future, the interests involved will become more and more complex.
Meng Qiuyan was also particularly happy at this time. It was the joy brought by being trusted, because Lu An told her frankly about such things.
She also knew the stakes involved. She could only talk about this kind of thing behind closed doors with Lu An. Not even her parents could reveal anything about it. This was why Lu An could feel free to talk to her about these things.
After a while, Meng Qiuyan looked at Lu An and couldn't help but smile and said: "I seem to see the scene where mathematicians and theoretical physicists all over the world are going crazy in the near future. I can't even understand it. Maybe my confidence will be hit, and I will even doubt my life."
Hearing this, Lu An smiled and said, "It's just that if you don't understand, you'll be very shocked, but if everyone can't understand, then you'll be relieved."
Everyone can't understand, which means it's not him, but Lu An is too strong.
(End of this chapter)