论文标题
Euler方程的二元混合模型的固定溶液。完整的频谱
Stationary solutions for dyadic mixed model of the Euler equation. A complete spectrum
论文作者
论文摘要
引入了Euler方程的二元模型作为玩具模型，以研究湍流理论中无粘性流体的行为。 1974年，诺维科夫（Novikov）提出了一个广义的混合二元模型，该模型扩展了katz-pavlovic和obukhov模型，生育了更复杂的结构：直到2015年，文献中才发现任何结果，在2015年之前，jeong I.J.显示了平滑解决方案的有限时间和对模型参数的特定值的自相似解决方案的存在。我们通过为两个有限的能量平稳溶液（即恒定且相似的溶液）提供完整的存在和独特结果来扩展这种部分结果。
Dyadic models of the Euler equations were introduced as toy models to study the behaviour of an inviscid fluid in turbulence theory. In 1974 Novikov proposed a generalized mixed dyadic model that extends both Katz-Pavlovic and Obukhov models giving birth to a more complex structure: no results were found in literature until 2015 where blow up in finite time for smooth solutions and existence of self-similar solution for particular values of the model parameters were shown by Jeong I.J. We extend such partial results by giving a complete spectrum of existence and uniqueness results for two cardinal classes of finite energy stationary solutions, namely constant and self-similar solutions.
