On the Kinetic Approach with Allowance for Higher-Order Heterogeneities in the Navier–Stokes Equation

A method for deriving the Navier–Stokes equation with allowance for inhomogeneities of any order on the Laplace operator using the Boltzmann kinetic equation is proposed. The solution method is based on the theory of nonequilibrium phenomena and the entropy growth principle. The calculation has been carried out to find additional inhomogeneous terms on the Laplace operator in the right-hand side of the Navier–Stokes equation. New-type fundamental solutions to the stationary parabolic equation have been predicted, which are significant for application in solving some problems of mathematical physics.