source:In early January 2014 the scientific world had spread sensational news. Press office of the Eurasian National University named after Gumilev in Almaty, said the director of the mathematical institute at the university Mukhtarbay Otelbaev (Mujtarbay Otelbayev) in Kazakh “Mathematical Journal” work titled “The existence of a strong solution of the Navier-Stokes equations.”
The Navier-Stokes equation is a mathematical equation that describes the motion of fluid substances, such as liquids and gases. It takes into account factors such as pressure, viscosity, and acceleration to predict the behavior of fluids in motion.
An exact solution for the Navier-Stokes equation would provide a complete understanding of how fluids behave in motion, allowing for more accurate predictions and simulations in various fields such as engineering, weather forecasting, and aerodynamics. It would also help in the development of new technologies and solutions for fluid-related problems.
One of the main challenges in finding an exact solution for the Navier-Stokes equation is its nonlinearity, which makes it difficult to solve using traditional mathematical methods. Additionally, the equation contains multiple unknown variables and boundary conditions, making it a complex problem to solve.
No, an exact solution for the Navier-Stokes equation has not been found yet. However, there have been several breakthroughs and advancements in the field, such as the Millennium Prize Problems, which offer a prize for anyone who can provide a solution to these equations.
Some of the current approaches to finding an exact solution for the Navier-Stokes equation include using numerical methods, such as finite element and finite difference methods, and developing new mathematical techniques and theories like the renormalization group theory. There is also ongoing research in using artificial intelligence and machine learning techniques to solve the Navier-Stokes equation.