On some dyadic models of the Euler equations
On some dyadic models of the Euler equations
复制标题
关于欧拉方程的一些二元模型
DOI：
10.1090/s0002-9939-06-08293-1
复制
发表时间：
2004
影响因子：
1.3
通讯作者：
F. Waleffe
中科院分区：
文献类型：
--
作者：
F. Waleffe
Katz和Pavlovic最近提出了一个Euler方程的并矢模型，证明了该模型在H3/2+∈ Sobolev范数下的有限时间爆破.结果表明，他们的模型可以减少到一个并矢模型的无粘Burgers方程。无粘Burgers方程在H α中，当α> 1/2时，表现出有限时间爆破，但它的并矢限制更加奇异，当α > 0时，表现出爆破。Friedlander和Pavlovic发展了一个密切相关的模型，他们也证明了H3/2+∈中的有限时间爆破。一些不一致的假设，在他们的模型的建设概述。对于包含所有这些模型的一类模型，证明了对任意a > 0，在H α范数下的有限时间爆破.讨论了Navier-Stokes方程的一种可供选择的壳模型。
Katz and Pavlovic recently proposed a dyadic model of the Euler equations for which they proved finite time blow-up in the H 3/2+∈ Sobolev norm. It is shown that their model can be reduced to a dyadic model of the inviscid Burgers equation. The inviscid Burgers equation exhibits finite time blow-up in H α , for a > 1/2, but its dyadic restriction is even more singular, exhibiting blow-up for any α > 0. Friedlander and Pavlovic developed a closely related model for which they also prove finite time blow-up in H 3/2+∈ . Some inconsistent assumptions in the construction of their model are outlined. Finite time blow-up in the H α norm, for any a > 0, is proven for a class of models that includes all those models. An alternative shell model of the Navier-Stokes equations is discussed.