an:01587988
Zbl 0973.35149
Brandolese, Lorenzo
On the localization of symmetric and asymmetric solutions of the Navier-Stokes equations in \(\mathbb{R}^n\)
EN
C. R. Acad. Sci., Paris, S??r. I, Math. 332, No. 2, 125-130 (2001).
00073259
2001
j
35Q30 35B30 76D05
space-time decay of solutions of the Navier-Stokes equations; localization condition; symmetries of small initial data
Summary: The aim of this note is to present some results on the space-time decay of solutions of the Navier-Stokes equations in \(\mathbb{R}^n\), with data \(u(0)= a\). We show that the localization condition \(L^1(\mathbb{R}^n,(1+|x|) dx)\) is instantaneously lost, during the Navier-Stokes evolution, if the data has non-orthogonal components with respect to the \(L^2\) inner product. We also show that some supplementary symmetries of small initial data allow us to obtain global strong solutions of the Navier-Stokes equations with an over-critical decay, both pointwise and of the energy norm.