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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 $\Omega\subset \bbfR^3$, 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.

35Q30Stokes and Navier-Stokes equations
35B35Stability of solutions of PDE
76D05Navier-Stokes equations (fluid dynamics)
76D55Flow control and optimization
93D20Asymptotic stability of control systems
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