Large, global solutions to the three-dimensional the navier-stokes equations without vertical viscosity
Analysis of PDEs
2022-02-24 v1
Abstract
The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main feature of which is that they are slowly varying in the direction where viscosity is missing. The difficulty arises from the complete absence of a regularising effect in this direction. The special structure of the nonlinear term, joint with the divergence-free condition on the velocity field, is crucial in obtaining the result.
Cite
@article{arxiv.2202.11536,
title = {Large, global solutions to the three-dimensional the navier-stokes equations without vertical viscosity},
author = {Isabelle Gallagher and Alexandre Yotopoulos},
journal= {arXiv preprint arXiv:2202.11536},
year = {2022}
}