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Application of Hardy space techniques to the time-decay problem for incompressible Navier-Stokes flows in $$\mathbb{R}^ n$$. (English) Zbl 1142.35544
From the introduction: This paper studies the large time behavior of weak and strong solutions to the incompressible Navier-Stokes system in $$\mathbb R^n$$, $$n\geq 2$$: .
$\partial_tu+ Au+ P(u\cdot\nabla u)=0 \quad (t>0), \qquad u(0)=a, \tag{NS}$
for unknown fluid velocity $$u$$ and an initial velocity $$a$$ given in $$L^2$$. We consider (NS) in the form of the integral equation. We establish a decay result for weak solutions in some “$$L^r$$-like space” with $$r<1$$.

##### MSC:
 35Q30 Navier-Stokes equations 35B35 Stability in context of PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids