Global regularity of three-dimensional density patches for inhomogeneous incompressible viscous flow

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（9）
• 页码范围: 1749-1764
• 页数: 16页
• 语种: 英文

摘要

Toward Lions' open question in Lions (1996) concerning the propagation of regularity for density patch,we prove that the boundary regularity of the 3-D density patch persists by time evolution for inhomogeneous incompressible viscous flows,with the initial density given by (1-η)1Ω0 + 1Ωc0 for some small enough constant η and some Wk+2,p domain Ω0,p ∈]3,∞[,and with the initial velocity satisfying some smallness condition and appropriate conormal regularities.