期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 -, 期 -, 页码 -出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2023040
关键词
Dimension theory; Poincare ' recurrences; multifractal analysis; discrete-time bifurcation
We investigate the asymptotic properties of the Boussinesq equations with vanishing thermal diffusivity in a bounded domain with no-slip boundary conditions. The dissipations of the L2 norm of velocity and its gradient, the convergence of the L2 norm of Au, and an o(1)-type exponential growth for IIA3/2uIIL2 are shown. Additionally, we obtain that the gradient of vorticity in the interior of the domain is bounded by a polynomial function of time.
We address the asymptotic properties for the Boussinesq equations with vanishing thermal diffusivity in a bounded domain with no-slip boundary conditions. We show the dissipation of the L2 norm of the velocity and its gradient, convergence of the L2 norm of Au, and an o(1)-type exponential growth for IIA3/2uIIL2. We also obtain that in the interior of the domain the gradient of the vorticity is bounded by a polynomial function of time.
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