New approach to interpretation of the nature of the Navier-Stokes equation and its solution - Статья

New approach to interpretation of the nature of the Navier-Stokes equation and its solution Altayev N.K. Kazakhstan, Shymkent Annotation The fundamental ideas of mathematical physics, which are accepted as the foundation in the attempt to solve the Navier-Stokes equation, by no means can be considered satisfactory, as the main results of the theory of infinite sets and theory of functions, developed as the direct consequence of the idea and results of this school, lead to obstacles. Certainly, in this state of affairs there is a basis for assumption, that trying to obtain the solutions from the Navier-Stokes equation it is more reasonable to interprete its nature based on the ideas developed in the field of theoretical and empricial physics. On the other hand, analysis has shown, that the development of the foundations of theoretical and empirical physics still remain not satisfactory to become the fundamental ideas developed in these field to be used to solve such problems. Based on joint analysis the fundamental ideas of scientific philosophy of Descartes and equations since the times of Descartes obtained on the basis of mathematics and physics, there was completed the principal part of development of the foundations of theoretical and empirical physics. Only after that the new ideas developed on this path were accepted as the foundation for the interpretation of the nature of the equations of Euler and Navier-Stokes, as the solutions having the meaning of solution, obtained from Newton equations with the accuracy inherent to algebraic physics. The nature of the Hagen-Poiseuille formula for which it is possible to obtain the proof based on Navier-Stokes equations, was interpreted as the solution obtained with the help inherent to arithmetic physics. New solutions, based on which it became possible to understand the nature of processes occurring in turbulent regime of flow, were obtained by generalization of Hagen-Poiseuille formula, while interpreting the nature of constants of viscosity based on the possibilities of new solutions, obtained from basic equations of statistical thermodynamics of Gibbs. 1. About the modern state of theoretical and empirical hydrodynamics and their difficulties As it is known, after the Newton equation was obtained (1) there was obtained the Euler equation (2) For ideal liquid and Navier-Stokes equation (3) For the non-ideal liquid, where: r - density, р - pressure, - vector of velocity, N - Nabla operator, h - kinetic viscosity, D - Laplace operator. After the analysis of experimental data by Hagen and Poiseuille there was obtained the expression of the form physics mathematical navier stokes (4) where: - energy expense, - pressure gradient, - tube radii; later it was shown, that based on equation (3) it is possible to obtain the analytic solutions, based on which it is possible to obtain the proof of (4). in the first case, and also the force Nр and force of resistance hDv in the second case. According to our views in order to think in such aspect, there should exist certain foundation that relations of Hagen and Poiseuille (4) at their time were obtained based on analysis of experimental data. That is why this relation has the meaning of solution, obtained for interrelationship between observed, i.e. measured values with the accuracy of empirical physics. Hence, the equations of mathematical physics (2) and (3), based on which it is possible to prove the relation (4) also should have the meaning of solution, obtained from equation of Newton (1).In other words, we believe, that until present time there was not obtained the satisfactory answer to the question of the following content. We believe, that if the correct answer is obtained, then based on new ideas and results, which were obtained on this path, it should become possible to correctly understand the true nature of equations (2) and (3). There is a basis to suppose that at their time equations and also all solutions of these equations were obtained by mathematicians with the goal to deeply understand the nature of : a) vibrational and wave processes; b) heat and diffusion processes. 3. On the question, why by analysis of ideas and equations, developed in the field of theoretical and empirical physics, we tried to obtain the answer to the question and why it was not possible to achieve this goal Here talking about the fundamental equations of theoretical physics, in general we have in mind the equation of dynamics of Newton (1) and equations of dynamics of Hamilton , (10) And also the fundamental equations of Hamilton-Jacobi-Schrodinger theory (11) And fundamental equations of statistical mechanics of Gibbs (12) where: Н - hamiltonian, S - action, y - wave function, V - potential energy, r - Gibbs probability density. Talking about the fundamental equations of empirical physics, we have in mind that the fundamental equations of Maxwell electrodynamics (13) And solutions of the type (14) Which are obtained from these