A necessary and sufficient condition for existence of measurable flow of a bounded borel vector field

Let b: [0, T] × ℝd → ℝd be a bounded Borel vector field, T > 0 and let µ be a non-negative Radon measure on ℝd. We prove that a µ-measurable flow of b exists if and only if the corresponding continuity equation has a non-negative measure-valued solution with the initial condition µ. © 2018 Independent University of Moscow.

Authors
Gusev N.A. 1, 2, 3
Journal
Moscow Mathematical Journal
Publisher
Independent University of Moscow
Number of issue
1
Language
English
Pages
85-92
Status
Published
Link
External link
Volume
18
Year
2018
Organizations
  • 1 Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina St, Moscow, 119991, Russian Federation
  • 2 Moscow Institute of Physics and Technology, 9 Institutskiy per, Moscow Region, Dolgoprudny, 141700, Russian Federation
  • 3 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
Keywords
Continuity equation; Flow; Measure-valued solutions; Non-smooth vector field; Ordinary differential equation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7280/
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