二维双扩散对流的长期动力学：分析与/或数值分析
Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics
AI总结：
研究二维双扩散对流模型的长期动力学，通过二阶显式格式时间离散化，推导连续和离散模型的统一界，证明吸引子和不变测度的存在，并分析离散模型在时间步长趋于零时向连续模型收敛的统计性质。
摘要：
我们考虑了一个二维双扩散对流模型及其使用二阶格式的时间离散化（采用 backward differentiation formula 与 one-leg 方法处理非线性项）。推导了连续和离散模型解的统一界（在离散模型的时间步长限制下），证明了吸引子和支撑在其上的不变测度的存在。作为结果，通过已建立的方法，可以得到离散模型在时间步长趋于零时吸引子的收敛性以及其长期统计性质向连续模型的收敛性。
英文摘要：
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. As a consequence, the convergence of the attractors and long time statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.
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