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Asymptotic stability for the 3D Navier-Stokes equations. (English) Zbl 1142.35548

Summary: We consider the 3D Navier-Stokes equations in \(\Omega\subset \mathbb{R}^3\), not necessarily bounded. We prove the asymptotic stability for weak solutions in the class \(\nabla u \in L^{\alpha}(0, \infty;L_{\gamma}(\Omega))\) for \(2/\alpha+3/\gamma=2\) with arbitrary initial and external perturbations.

MSC:

35Q30 Navier-Stokes equations
35B35 Stability in context of PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76D55 Flow control and optimization for incompressible viscous fluids
93D20 Asymptotic stability in control theory
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