A simple Monte Carlo method for solving of Navier-Stokes Equations

TL;DR

This paper introduces a straightforward Monte Carlo approach to numerically solve multidimensional Navier-Stokes equations with initial and boundary conditions in unbounded space, applicable when data are in specific Sobolev-Lebesgue-Riesz spaces.

Contribution

It presents a novel, simple Monte Carlo method tailored for solving multidimensional Navier-Stokes equations with initial and boundary conditions in unbounded space.

Findings

Method effectively handles multidimensional problems.

Applicable to initial value and non-homogeneous boundary conditions.

Works with data in Sobolev-Lebesgue-Riesz spaces.

Abstract

We offer a simple Monte-Carlo method for solving of the multidimensional initial value and non-homogeneous problem for the Navier-Stokes Equations in whole space when the initial function and right hand side belong to the correspondent Sobolev-Lebesgue-Riesz space.