Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance
Tóm tắt
This paper focuses on the three-dimensional (3D) incompressible anisotropic Boussinesq system with horizontal dissipation. The goal here is to assess the stability property and pinpoint the precise large-time behavior of perturbations near the hydrostatic balance. Important tools such as Schonbek’s Fourier splitting method have been developed to understand the large-time behavior of PDE systems with full dissipation, but these tools may not apply directly when the systems are only partially dissipated. This paper solves the stability problem and designs an effective approach to obtain the optimal decay rates for the anisotropic Boussinesq system concerned here. The tool developed in this paper may be useful for many other partially dissipated systems.
Tài liệu tham khảo
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