论文标题
野生霍德 - 连续解决方案的规律性时期
Epochs of regularity for wild Hölder-continuous solutions of the Hypodissipative Navier-Stokes System
论文作者
论文摘要
我们考虑$ [0，t] \ times \ mathbb {t}^{d} $上的缩写Navier-Stokes方程，并寻求构建非唯一的，Hölder-continuul的解决方案，具有规律性的时期（使用CONVEX Integration Techniques，几乎平稳的是平滑的，几乎在时间外部的小单台词设置）。特别是，我们提供了分数拉普拉斯的力量，奇异集的维度与解决方案的规律性之间的定量关系。此外，我们还将通常的矢量计算参数推广到具有拉格朗日坐标的更高维度。
We consider the hypodissipative Navier-Stokes equations on $[0,T]\times\mathbb{T}^{d}$ and seek to construct non-unique, Hölder-continuous solutions with epochs of regularity (smooth almost everywhere outside a small singular set in time), using convex integration techniques. In particular, we give quantitative relationships between the power of the fractional Laplacian, the dimension of the singular set, and the regularity of the solution. In addition, we also generalize the usual vector calculus arguments to higher dimensions with Lagrangian coordinates.
