Global regularity of three dimensional density patch for inhomogeneous incompressible viscous flow

TL;DR

This paper proves that the boundary regularity of a 3D density patch remains intact over time in inhomogeneous incompressible viscous flow, given certain initial velocity conditions.

Contribution

It establishes the persistence of boundary regularity for 3D density patches in viscous flows, extending understanding of interface stability in fluid dynamics.

Findings

Boundary regularity persists over time.

Small initial velocity condition is crucial.

Advances the theory of density interface evolution.

Abstract

The present work is devoted to proving that the boundary regularity of the three dimensional density patch persists by time evolution for inhomogeneous incompressible viscous flow, with some smallness condition on the initial velocity.