无粘二元模型中正向能量级联的正则化效应
偏微分方程分析
2014-03-03 v4
摘要
我们研究了欧拉方程的无粘二元模型，并证明了由于正向能量级联，非线性项具有某些正则化性质。我们证明每个解在任意正时间都必须具有3/5的L^2基（或1/10的L^3基）正则性。我们推测这一结果在Onsager尺度下仍然成立，此时L^2基指数为5/6，L^3基指数为1/3。
引用
@article{arxiv.1310.7612,
title = {Regularizing Effect of the Forward Energy Cascade in the Inviscid Dyadic Model},
author = {Alexey Cheskidov and Karen Zaya},
journal= {arXiv preprint arXiv:1310.7612},
year = {2014}
}
备注
13 pages, 2 figures. Corrected misprints, added a new reference, elaborated on how the final bound for Theorem 4.2 was achieved, and specified assumption about positive solutions earlier in the paper