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Asymptotic stability of large solutions with large perturbation to the Navier-Stokes equations. (English) Zbl 0970.35106
The author considers the asymptotic stability of $$w$$, the strong (Serrin’s class) solution of the Navier-Stokes equations in a domain $$\Omega\subseteq \mathbb{R}^3$$ of class $$C^3$$, not necessarily bounded. He proves that if $$v$$ is a weak perturbed solution then the norm of $$(w-v)$$ in $$L^2(t,t+ 1,L^2(\Omega))$$ tends to zero as $$t\to\infty$$ if $$v$$ satisfies the stronger form of the energy inequality. Finally, he obtains explicit rates of convergence for some specific perturbations.

##### MSC:
 35Q30 Navier-Stokes equations 76E09 Stability and instability of nonparallel flows in hydrodynamic stability 76D05 Navier-Stokes equations for incompressible viscous fluids
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##### References:
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