Spatial decay of the velocity field of an incompressible viscous fluid in image Original Research Article

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 View the MathML sourceLp(Rd;(1+|x|)pϑdx) Turn MathJax on with p>dp>d, ϑ⩾0ϑ⩾0 and equation(⋆) View the MathML sourceϑ+dp