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This article is cited in 2 scientific papers (total in 2 papers)
A necessary and sufficient condition for existence of measurable flow of a bounded Borel vector field
Nikolay A. Gusevabc a Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina St, Moscow, 119991
b Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700
c RUDN University, 6 Miklukho-Maklay St, Moscow, 117198
Abstract:
Let $b\colon[0,T]\times\mathbb R^d\to\mathbb R^d$ be a bounded Borel vector field, $T>0$ and let $\bar\mu$ be a non-negative Radon measure on $\mathbb R^d$. We prove that a $\bar\mu$-measurable flow of $b$ exists if and only if the corresponding continuity equation has a non-negative measure-valued solution with the initial condition $\bar\mu$.
Key words and phrases:
continuity equation, non-smooth vector field, measure-valued solutions, flow, ordinary differential equation.
Citation:
Nikolay A. Gusev, “A necessary and sufficient condition for existence of measurable flow of a bounded Borel vector field”, Mosc. Math. J., 18:1 (2018), 85–92
Linking options:
https://www.mathnet.ru/eng/mmj648 https://www.mathnet.ru/eng/mmj/v18/i1/p85
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Abstract page: | 193 | References: | 46 |
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