Naville-Stokes equation, the ups and downs of waves follow our boat winding across the lake, and the turbulent airflow follows the flight of our modern jet plane. Mathematicians and physicists are convinced that both breeze and turbulence can be explained and predicted by understanding the solution of Naville-Stokes equation.

Although these equations were written in19th century, we still know little about them. The challenge is to make substantial progress in mathematical theory, so that we can solve the mystery hidden in Naville-Stokes equation.

Without a head or tail, even in this passage, it is difficult for you to guess what the problem really describes, revealing a metaphysical problem. Today, we will discuss the Naville-Stokes equation.

This equation was not put forward by one person. 1775, the famous mathematician Euler, yes, is the four kings of mathematics. Now he has mixed fluid mechanics. In his book "General Principles of Fluid Motion", he deduced a set of equations according to the changes of force and momentum of fluid when inviscid fluid is moving.

The equation is as follows: (axD+bxD+c)y=f(x) (there is only one form, and the differential expression of functional extreme conditions, etc. ), which is the most important basic equation in inviscid fluid dynamics (ideal fluid dynamics), refers to the differential equation of motion obtained by applying Newton's second law to inviscid fluid micelles, and describes the motion law of ideal fluid. It laid the foundation of ideal fluid mechanics.

Viscous fluid refers to a fluid whose viscosity effect cannot be ignored. The actual fluid in nature is viscous, so the actual fluid is also called viscous fluid, which refers to the property that the active layer between fluid particles generates friction due to relative motion and resists relative motion.

Introduction to mathematics:

Mathematics [English: Mathematics, from ancient Greece μ? θξμα(máthēma)； Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information.

Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.

Structure:

Many mathematical objects, such as numbers, functions, geometry, etc., reflect the internal structure of continuous operation or the relationships defined therein. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations.

In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures. Therefore, we can learn abstract systems such as groups, rings and domains.

These studies (structures defined by algebraic operations) can form the field of abstract algebra. Because abstract algebra has great universality, it can often be applied to some seemingly unrelated problems. For example, some problems of drawing rulers and rulers in ancient times were finally solved by Galois theory, which involved the theory of presence and group theory.

Another example of algebraic theory is linear algebra, which makes a general study of vector spaces with quantitative and directional elements. These phenomena show that geometry and algebra, which were originally considered irrelevant, actually have a strong correlation. Combinatorial mathematics studies the method of enumerating several objects satisfying a given structure.