Global solutions of the random vortex filament equation

被引：4

作者：

Brzezniak, Z. ^{[1
]}

Gubinelli, M. ^{[2
,3
]}

Neklyudov, M. ^{[1
]}

机构：

[1] Univ York, Dept Math, Heslington, Yorks, England

[2] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

[3] Univ Paris 09, CNRS, UMR 7534, F-75775 Paris 16, France

来源：

NONLINEARITY | 2013年 / 26卷 / 09期

关键词：

VORTICITY; EVOLUTION;

D O I：

10.1088/0951-7715/26/9/2499

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of a global solution for the filament equation with the inital condition given by a geometric rough path in the sense of Lyons (1998 Rev. Mat. Iberoamericana 14 215-310). Our work gives a positive answer to a question left open in recent publications: Berselli and Gubinelli (2007 Commun. Math. Phys. 269 693-713) showed the existence of a global solution for a smooth initial condition while Bessaih et al (2005 Ann. Probab. 33 1825-55) proved the existence of a local solution for a general initial condition given by a rough path.

引用

页码：2499 / 2514

页数：16

共 20 条

[1]

Arnold V. I., 1998, Topological Methods in Hydrodynamics

[2] REMARKS ON THE BREAKDOWN OF SMOOTH SOLUTIONS FOR THE 3-D EULER EQUATIONS [J].