Strong Solution of Modified Anistropic 3D-Navier-Stokes Equations

TL;DR

This paper establishes a strong solution for the modified anisotropic 3D-Navier-Stokes equations with a logarithmic damping term, using novel methods and Fourier analysis in a fractional Sobolev space.

Contribution

It introduces new analytical techniques and tools to prove the existence of strong solutions for a modified Navier-Stokes model with logarithmic damping.

Findings

Existence of strong solutions in $H^{0.1}$ space.

Application of Fourier analysis to anisotropic Navier-Stokes equations.

Development of new methods for handling logarithmic damping terms.

Abstract

In this paper we study the anisotropic incompressible Navier-Stokes equations with a logarithm damping $\alpha \log(e+|u|^2)|u|^2u$ in $H^{0.1}$, where we used new methods, new tools and Fourier analysis.