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Generating and Adding Flows on Locally Complete Metric Spaces

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Abstract

As a generalization of a vector field on a manifold, the notion of an arc field on a locally complete metric space was introduced in Bleecker and Calcaterra (J Math Anal Appl, 248: 645–677, 2000). In that paper, the authors proved an analogue of the Cauchy–Lipschitz Theorem, i.e they showed the existence and uniqueness of solution curves for a time independent arc field. In this paper, we extend the result to the time dependent case, namely we show the existence and uniqueness of solution curves for a time dependent arc field. We also introduce the notion of the sum of two time dependent arc fields and show existence and uniqueness of solution curves for this sum.

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Acknowledgments

N. M was partially supported by an NSF Grant DMS-1211806.

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Authors and Affiliations

  1. Institute of Mathematical Sciences, Ewha Wonans University Helen Building, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul, South Korea

    Hwa Kil Kim

  2. Courant Institute, New York University, 251 Mercer street, New York, NY, 10012, USA

    Nader Masmoudi

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  1. Hwa Kil Kim
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  2. Nader Masmoudi
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Correspondence to Hwa Kil Kim.

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Kim, H.K., Masmoudi, N. Generating and Adding Flows on Locally Complete Metric Spaces. J Dyn Diff Equat 25, 231–256 (2013). https://doi.org/10.1007/s10884-012-9280-3

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  • DOI: https://doi.org/10.1007/s10884-012-9280-3

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