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On the determining wavenumber for the nonautonomous subcritical SQG equation. (English) Zbl 1446.35121

Summary: A time-dependent determining wavenumber was introduced in [the authors, Physica D 376–377, 204–215 (2018; Zbl 1398.35162)] to estimate the number of determining modes for the surface quasi-geostrophic equation. In this paper we continue this investigation focusing on the subcritical case and study trajectories inside an absorbing set bounded in \(L^\infty\). Utilizing this bound we find a time-independent determining wavenumber that improves the estimate obtained in [loc. cit.]. This classical approach is more direct, but it is contingent on the existence of the \(L^\infty\) absorbing set.

MSC:

35Q35 PDEs in connection with fluid mechanics
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35B41 Attractors
35Q86 PDEs in connection with geophysics
86A05 Hydrology, hydrography, oceanography

Citations:

Zbl 1398.35162
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References:

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