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

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 flow, with the initial density given by ( 1 − η ) 1 Ω 0 + 1 Ω 0 c...

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Bibliographic Details
Published in:Science China. Mathematics 2019-09, Vol.62 (9), p.1749-1764
Main Authors: Liao, Xian, Liu, Yanlin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Density
Fluid flow
Incompressible flow
Mathematics
Mathematics and Statistics
Regularity
Viscous flow
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Summary: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 flow, with the initial density given by ( 1 − η ) 1 Ω 0 + 1 Ω 0 c for some small enough constant η and some W k+2, p domain Ω 0 , p ∈]3,∞[, and with the initial velocity satisfying some smallness condition and appropriate conormal regularities.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-017-9196-7