Abstract
The interrelation between analytic functions and real-valued functions is formulated in the work. It is shown such an interrelation realizes nonlinear representations for real-valued functions that allow to develop new methods of estimation for them. These methods of estimation are approved by solving the Cauchy problem for equations of viscous incompressible liquid.
Highlights
The problem of over-determination in the multi-dimensional inverse problem of quantum scattering theory is obviated since a potential can be defined by amplitude averaging when the amplitude is a function of three variables
In the classic case of the multi- dimensional inverse problem of quantum scattering theory the potential requires restoring with respect to the amplitude that depends on five variables
Further detalization could have distracted us from the general research line of the work consisting in application of energy and momentum conservation laws in terms of wave functions to the theory of nonlinear equations
Summary
The first results obtained by the author are described in the works [1,2,3]. This problem includes a number of subproblems which appear to be very interesting and complicated. The latest advances in the theory of SIPM (Scattering Inverse Problem Method) were a great stimulus for the author as well as other researchers. Another important stimulus was the work of M. The basic aim of the paper is to study this interrelation and its application for obtaining new estimates to the solutions of the problem for Navier-Stokes’ equations. The effectiveness and novelty of the obtained results are displayed when solving the notoriously difficult Chauchy problem for Navier-Stokes’ equations of viscous incompressible fluid
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