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

2015/10/25 by Durmagambetov, A. A.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1510.07235

Abstract

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.

Related

• Global existence, uniqueness and estimates of the solution to the Navier-Stokes equations
• Exact solutions to the Navier-Stokes equation for an incompressible flow from the interpretation of the Schroedinger wave function
• Weak Solutions of Navier-Stokes equations through bounded operators
• Scattering Amplitudes and the Navier-Stokes Equation
• Global in time solvability of the Navier-Stokes equations in the half-space