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Dynamical properties of spatially non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite strip. (English) Zbl 1062.35057

Summary: The main result of this paper is the global well-posedness of the Cauchy problem to the 2D Navier-Stokes system with the initial data \(u_0 \in \text{BUC}(\mathbb O)\) and the external force \(F \in C([0,\infty), L^\infty(\mathbb O))\) on the manifold \(\mathbb O= \mathbb R \times \mathbb S^1\), i.e., the fluid flow is supposed to be periodic in one of the spatial directions whereas in the unbounded direction only uniform boundedness is assumed. However, to obtain uniqueness we need to make assumptions which suppress additional pressure gradients. For this aim Riesz operators on \(\text{L}^\infty(\mathbb O)\) are used to define \(p(t) \in \text{BMO}(\mathbb O)\). For time-independent forces the solutions are shown to grow at most cubically in the time \(t\).

MSC:

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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