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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 $\Omega\subseteq \bbfR^3$ 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:
35Q30Stokes and Navier-Stokes equations
76E09Stability and instability of nonparallel flows
76D05Navier-Stokes equations (fluid dynamics)
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References:
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