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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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