The Ginzburg-Landau formalism for pattern forming systems with conservation laws

具有守恒定律的模式形成系统的金兹堡-朗道形式主义

• 批准号: 421289701
• 负责人: Professor Dr. Guido Schneider
• 金额: --
• 依托单位: Lehrstuhl für Analysis und Modellierung
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/421289701?language=en
• 关键词: Ginzburg; Landau; formalism; pattern; forming

We consider pattern-forming systems with conservation laws in infinitely long cylindrical domains near the first instability.With the help of a multi-scale ansatz, Ginzburg-Landau like amplitude systems can be derived. They will be used to show the global existence of solutions near the unstable origin.The new difficulty is the missing absorbent ball due to the conservation laws.Applications are the Marangoni problem, the flow down an inclined plane, or the Faraday Problem.

考虑无限长圆柱区域中第一不稳定性附近具有守恒律的斑图形成系统，借助于多尺度分析，可以得到Ginzburg-Landau型振幅系统。新的困难是由于守恒律而丢失了吸收球，应用是Marangoni问题，沿斜面向下的流动，或法拉第问题。