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• W4320712507 abstract "We consider the incompressible hyperdissipative Navier–Stokes equations begin{align}left {begin{array}{l} u_t+epsilon (-Delta )^alpha u+(ucdot nabla )u+nabla p=f, nabla cdot u=0, end{array} right .end{align} on a two- or three-dimensional periodic torus, where the power and the forcing function is time-dependent. We intend to reveal how the fractional dissipation and the time-dependent force affect long-time dynamics of weak solutions. More precisely, we prove that with certain conditions on , there exists a finite-dimensional Lipschitz manifold in the -space of divergent-free vector fields with zero mean. The manifold is locally forward invariant and pullback exponentially attracting. Moreover, the compact uniform attractor is contained in the union of all fibers of the manifold. In our result, no large viscosity is assumed. It is also significant that in the three-dimensional case the spectrum of the fractional Laplacian does not have arbitrarily large gaps." @default.
• W4320712507 created "2023-02-15" @default.
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• W4320712507 date "2023-02-15" @default.
• W4320712507 modified "2023-10-14" @default.
• W4320712507 title "Hyperdissipative Navier–Stokes Equations Driven by Time-Dependent Forces: Invariant Manifolds" @default.
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• W4320712507 doi "https://doi.org/10.1137/22m1470323" @default.
• W4320712507 hasPublicationYear "2023" @default.
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