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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 \(r<1\).

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