Abstract
In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.
Highlights
We present final solving Millennium Prize Problems formulated by Clay Math
The Navier-Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier-Stokes equations
Since understanding the Navier-Stokes equations is considered to be the first step to understanding the elusive phenomenon of turbulence, the Clay Mathematics Institute in May 2000 made this problem one of its seven Millennium Prize problems in mathematics
Summary
We present final solving Millennium Prize Problems formulated by Clay Math. For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proved that smooth solutions always exist, or that if they do exist, they have bounded energy per unit mass This is called the Navier-Stokes existence and smoothness problem. We consider some ideas for the potential in the inverse scattering problem, and this is used to estimate of solutions of the Cauchy problem for the Navier-Stokes equations. We consider the three-dimensional inverse scattering problem for the Schrödinger operator: the scattering potential must be reconstructed from the scattering amplitude This problem has been studied by a number of researchers [9] [11] [12] and references therein
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