Spatial decay of the velocity field of an incompressible viscous fluid in

✍ Scribed by François Vigneron

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 289 KB
• Volume: 63
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.05.016

✦ Synopsis

This article proves that mild solutions to the Navier-Stokes equations can be relatively well localised in the physical space and analyses which localisation methods are actually acceptable. In brief, if the initial velocity belongs to a weighted Lebesgue space like

then so does the associated strong solution, as long as it exists in L p . The ( ) condition cannot generically be improved, because the stability of any opposite case requires exceptional symmetry properties in the velocity field. This work is closely related to recent studies of L. Brandolese and Y. Meyer.