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)1?0+ 1?0c for some small enough constant η and some Wk+2p,domain ?0, p ∈]3, ∞[, and with the initial velocity satisfying some smallness condition and appropriate conormal regularities.
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）1?0+ 1?0c for some small enough constant η and some Wk+2p,domain ?0, p ∈]3, ∞[, and with the initial velocity satisfying some smallness condition and appropriate conormal regularities.
基金
supported by Collaborative Research Centre 1060,University of Bonn
