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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 Ω 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 (Ω)) tends to zero as t if v satisfies the stronger form of the energy inequality. Finally, he obtains explicit rates of convergence for some specific perturbations.
35Q30Stokes and Navier-Stokes equations
76E09Stability and instability of nonparallel flows
76D05Navier-Stokes equations (fluid dynamics)