对流层波传播模型的适定性与长期行为
Well-posedness and long-term behaviour for a troposphere wave propagation model
AI总结：
研究对流层波传播模型（含晨辉云图案）的适定性与长期行为，引入新压力项后证明全局适定性与吸引子存在，并指出参数范围影响解的有界性。
摘要：
本文研究A. Constantin和R.S. Johnson近期提出的对流层非线性波传播模型，特别是“晨辉”云图案。我们考虑在对流层顶部对垂直速度施加自然Dirichlet边界条件的模型，并由此引入新的压力项。该修正系统与二维原始方程存在结构联系，后者已知具有全局适定性和全局吸引子的存在性。我们将这些结果转移到修正模型上，给出利用特定特征并结合标准方法与各向异性Sobolev不等式的证明。此外，我们表明吸引子仅对特定参数范围存在，而对于其他参数，我们发现随时间无界增长的失控解。
英文摘要：
In this paper, we investigate a model recently derived by A. Constantin and R.S. Johnson for nonlinear wave propagation in the troposphere, particularly the 'morning glory' cloud pattern. We consider the model with natural Dirichlet boundary conditions for the vertical velocity at the top of the troposphere, and thus introduce a new pressure term. This modified system has a structural relation to the 2D primitive equations, for which global well-posedness and the existence of a global attractor are already known. We transfer these results to the modified model, giving proofs that exploit specific features and use standard methods combined with anisotropic Sobolev inequalities. Additionally, we show that the attractor exists only for specific parameter ranges, while for other parameters, we find runaway solutions with unbounded growth over time.
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