| Abstract: |
| We study the asymptotic behavior of small global solutions to the incompressible Navier-Stokes system. It is known that a suitable spatial decay allows the global solution to behave like self-similar solutions as time goes to infinity (Kato(1984), Planchon(1998)}).
More precisely, if the spatial decay of the initial data is critical (i.e., $\varphi(x) = O(|x|^{-1})$)
then the solution is asymptotic to a nonlinear self-similar solution,
and if not, then the solution is asymptotic a linear self-similar solution.
Under minimal assumptions on the initial data, we revisit this classical result on
asymptotically self-similar solutions, and derive the second asymptotic expansion.
The result can be extended to multiplier-type weighted Lorentz spaces. |
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