A NECESSARY AND SUFFICIENT CONDITION FOR EXISTENCE OF MEASURABLE FLOW OF A BOUNDED BOREL VECTOR FIELD

被引：2
|
作者：
Gusev, Nikolay A. [1 ,2 ,3 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, 8 Gubkina St, Moscow 119991, Russia
[2] Moscow Inst Phys & Technol, 9 Inst Skiy Per, Dolgoprudnyi 141700, Moscow Region, Russia
[3] RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia
来源：
MOSCOW MATHEMATICAL JOURNAL | 2018年 / 18卷 / 01期
关键词：
Continuity equation; non-smooth vector field; measure-valued solutions; flow; ordinary differential equation;
D O I：
10.17323/1609-4514-2018-18-1-85-92
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let b: [0, T] x R-d -> R-d be a bounded Borel vector field, T > 0 and let (mu) over bar be a non-negative Radon measure on R-d. We prove that a (mu) over bar -measurable flow of b exists if and only if the corresponding continuity equation has a non-negative measure-valued solution with the initial condition (mu) over bar.
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页码：85 / 92
页数：8
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