Axisymmetric Rotating Fluid Equations

TL;DR

This paper studies the mathematical properties of axisymmetric rotating viscous fluid equations, proving local existence and regularity propagation in anisotropic Sobolev spaces, relevant for understanding fluid behavior in rotating cylindrical domains.

Contribution

It establishes uniform local existence results and regularity propagation for anisotropic axisymmetric viscous fluids in rotating cylindrical settings, with respect to the Rossby number.

Findings

Proved uniform local existence in anisotropic Sobolev spaces.

Established propagation of isotropic Sobolev regularity.

Analyzed equations in the exterior of a rotating cylinder.

Abstract

We investigate the equations of anisotropic axisymmetric incompressible viscous fluids in the exterior of a cylinder of $\R^3$, rotating around an inhomogeneous vector $B(t, r)$. We prove uniform local existence with respect to the Rossby number in suitable anisotropic Sobolev spaces. We also obtain the propagation of the isotropic Sobolev regularity.