无粘并矢模型中前向能量级联的正则化效应
Regularizing Effect of the Forward Energy Cascade in the Inviscid Dyadic Model
摘要：
研究了欧拉方程的无粘并矢模型，证明了由于前向能量级联而引起的非线性项的正则化性质。我们证明了对于所有正时间，每个解都必须具有3/5 L^2基（或1/10 L^3基）正则性。我们推测这符合昂萨格标度，其中基于L^2的指数是5/6，基于L^3的指数是1/3。
英文摘要：
We study the inviscid dyadic model of the Euler equations and prove some regularizing properties of the nonlinear term that occur due to forward energy cascade. We show every solution must have 3/5 L^2-based (or 1/10 L^3-based) regularity for all positive time. We conjecture this holds up to Onsager's scaling, where the L^2-based exponent is 5/6 and the L^3-based exponent is 1/3.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
