arXiv subjects

A. A. Durmagambetov

Publications and source records attributed to A. A. Durmagambetov.

4 recordsLinked to original sources

arXiv2019

Poincare--Riemann--Hilbert boundary-value problem for The Millennium Prize Problems

Using the example of a complicated problem such as the Cauchy problem for the Navier--Stokes equation, we show how the Poincaré--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of solutions for this case. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincaré--Riemann--Hilbert boundary-value problem. The same scheme of reduction of Riemann integral equations for the zeta function to the Poincaré--Riemann--Hilbert boundary-value problem allows us to construct effective estimates that describe the behaviour of the zeros of the zeta function very well.

math.GM↗

arXiv2018

New global estimations of the Cauchy problem for the Navier-Stokes equations

Using the example of such a complicated problem as the Cauchy problem for the Navier-Stokes equation, we show how the Poincaré-Riemann-Hilbert boundary value problem enables us to construct effective estimates of solutions for this case. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developing for this. In which it is shown that the unitary scattering operator can be studied as a solution of the Poincaré-Riemann-Hilbert boundary-value problem. This allows us to go on to study the potential in the Schrodinger equation, which we consider as a velocity component in the Navier-Stokes equation. The same scheme of reduction of Riemann integral equations for the zeta-function to the Poincaré-Riemann-Hilbert boundary-value problem allows us to construct effective estimates that describe the behavior of the zeros of the zeta function very well.

math-ph↗

arXiv2016

Infinitely many twin primes

In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins

math.GM↗

arXiv2016

A gradient catastrophe mechanism in contexts of the phase change condition

The paper describes the mechanism of occurrence of a gradient catastrophe when changing phase. Materials shows that classical methods of estimation theory of functions do not fit the problem of studying the gradient catastrophe. We present material showing that the embedding theorem can not give an opportunity to study the process of a gradient catastrophe. In fact, work justifies pessimism Terence Tao in the insolvency of modern mathematics to solve the problem of the Navier-Stokes equations. It is suggested an alternative method for studying the gradient catastrophe through the study of the Fourier transform function through special properties phases of the Fourier transform of this function

math.GM↗