Method of Two-dimensional Nonlinear Laplace Transformation for Solving the Navier – Stokes Equation

Abstract

This paper introduces a new nonlinear
Laplace transforms allowing to reduce the Navier – Stokes
equation to ordinary Riccati’s one. It is mathematically
proved that the no-linear summand
d z
v d v in the Navier –
Stokes equation can be reduced to that expressing the
multiplication of the operators f1o (ξ ,t ) ⋅ f2o (ξ ,t ) , where
the functions f1o (ξ ,t ) and f2o (ξ ,t ) are images of the
functions v and
d z
d v
, correspondingly. Such an approach
gives the opportunity to get analytical solution of the
problem of viscous fluid motion in a pipe. The algorithm
may be used to solve the majority of algebraic nonlinear
problems of mathematical physics.