Nonuniqueness of Solutions to the Euler Equations with Vorticity in a Lorentz Space

被引：8

作者：

Brue, Elia ^{[1
,2
]}

Colombo, Maria ^{[3
]}

机构：

[1] Inst Adv Study, 1 Einstein Dr, Princeton, NJ 05840 USA

[2] Bocconi Univ, Milan, Italy

[3] EPFL B, Stn 8, CH-1015 Lausanne, Switzerland

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 403卷 / 02期

关键词：

D O I：

10.1007/s00220-023-04816-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

For the two dimensional Euler equations, a classical result by Yudovich states that solutions are unique in the class of bounded vorticity; it is a celebrated open problem whether this uniqueness result can be extended in other integrability spaces. We prove in this note that such uniqueness theorem fails in the class of vector fields u with uniformly bounded kinetic energy and vorticity in the Lorentz space L-1,L-8.

引用

页码：1171 / 1192

页数：22

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