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

我们考虑在第一不稳定性附近的无限长圆柱形区域中具有守恒律的模式形成系统。借助多尺度分析，可以推导出类金兹堡-朗道振幅系统。它们将用于证明解在不稳定原点附近的全局存在性。新的难点是由于守恒定律导致的吸收球缺失。应用是马兰戈尼问题，沿斜面流动，或法拉第问题。

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.