The large-time energy concentration in solutions to the Navier–Stokes equations in the frequency space

Skalák, Zdenĕk

doi:10.1016/j.jmaa.2012.11.004

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…In [194] it is shown that frequencies tend to concentrate on an arbitrary small annulus (a > 0) or ball (a = 0) as t → ∞. In particular it is established that for such weak solutions, which are non zero for times lager than some T ≥ 0…”

Section: Further Applications Of Besov Spaces and Z Skalák Analysis mentioning

confidence: 99%

“…A lower bound of decay is obtained for any γ ∈ (0, Notice that (37) provides information on the long time behavior of frequencies. In a series of papers (see [194] and the references therein) Z. Skalák gave new insight on the large time behavior of the solutions. He showed that a certain frequency concentration effect occurs for weak solutions with zero external forces, satisfying the strong energy inequality (5).…”

Section: Further Applications Of Besov Spaces and Z Skalák Analysis mentioning

confidence: 99%

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Large Time Behavior of the Navier-Stokes Flow

Brandolese

Schonbek

2018

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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Different results related to the asymptotic behavior of incompressible fluid equations are analyzed as time tends to infinity. The main focus is on the solutions to the Navier-Stokes equations, but in the final section a brief discussion is added on solutions to Magneto-Hydrodynamics, Liquid crystals, Quasi-Geostrophic and Boussinesq equations. Consideration is given to results on decay, asymptotic profiles, and stability for finite and nonfinite energy solutions.

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Section: Further Applications Of Besov Spaces and Z Skalák Analysis mentioning

confidence: 99%

Section: Further Applications Of Besov Spaces and Z Skalák Analysis mentioning

confidence: 99%