The topics of the present issue of our journal are addressing the problem of longevity and a healthy life. We open our topical discussion with a unique article presenting new data on the performance of the cardiovascular system in individuals aged over 90. We are sure it will contribute to a better understanding of some specific age-related features in a human organism. The other papers of outstanding scientists published herein should complete our analysis of challenges associated with longevity and prolongation of human life.
And there is one more fascinating important message for our readership: S.G. Chefranov, our Editorial Board Member, Doctor of Physical and Mathematical Sciences, devotes most of his research efforts to hemodynamics treated by him from the standpoint of mathematics. His papers are often found in our journal, and they always offer an excellent mathematical analysis of blood circulation processes in a human body. The most accurate description of hemodynamics as an integral part of hydrodynamics is developed by him in the context of the Navier-Stokes equations. The said equations are considered as very complicated, so that till the present no analytical solution for any moment of time has been found. Moreover, the equations are considered as much too complicated to be soluble for arbitrary smooth initial conditions. At the same time, the Navier-Stokes (NS) equation is widely used for numerical modeling in various fields of applications: from non-stationary vortex air flows in aircraft designing up to forecasting of weather phenomena that is of great importance for aviation, industry in general and even human health. However, at present, errors in computation and prediction based on the NS equation cannot be systematically realized and reduced because of the absence of not only a smooth analytical solution, but even the proof of the existence of such solution for any finite time to the three-dimensional (3D) Navier-Stokes equation. The problem of establishing this proof for the 3D Navier-Stokes equation (for a relatively simple approximation, where the described medium is regarded as incompressible one) is included into the list of seven fundamental unresolved mathematical problems of the Millennium formulated by the Clay Mathematical Institute (USA). And now, it gives us great pleasure to announce that our Editorial Board has received a fresh article by S.G. Chefranov, co-authored with his son, where their original analytical smooth solution to the 3D Navier-Stokes equation is offered, covering even the most complicated description case: vortex flows of the viscous compressible medium (actually, all media are compressible with varying degrees). It is undeniably a huge success! Moreover, the elegance of the found solution supports the well-known principle in science: the true discovery always implies beauty and elegance both from the viewpoints of scientific logics and mathematics!
Our Readers should notice that, when deriving the hemodynamic equations by G.M. Poyedintsev - O. K. Voronova, which form the foundation of the theory of cardiometry, a new structural mode of the fluid flow was discovered, which was given the name "the third flow mode" to differ it from the well-known laminar and turbulent ones. The third flow mode is characterized by minimized energy consumptions. By this means evidence has been submitted that the purpose of the performance of the entire cardiovascular system is to generate and properly maintain the third mode of the blood flow in our organism. The discovery has given impetus to creating a new fundamental science: cardiometry.
Most attention has been concentrated by S.G. Chefranov on the mathematical description of specific features of the third flow mode using the Navier-Stokes equation. And now we are prepared to present his new paper where the credit for the solution of one of the above seven Millenium problems is given to S.G.Chefranov and his son. It turns out the two topics of primary concern: the NS equation in mathematics and human hemodynamics are very closely related subjects. This excellent scientific achievement deserves respect and recognition! So, it might be thought that we deal not only with an outstanding scientific achievement, but also with a highly promising research tool for further development of the theory of cardiometry.
There is no doubt the pioneering advancements of our scientists will make a great contribution to the development of research methodology in natural sciences in general.
We are sure this issue of the journal will not have gone unnoticed by the research community, and the hot topics hereof will have all the chances of receiving ample interest by those who is acquiring knowledge, expertise and understanding through thought and experience in science.