Ohkitani, K. (2017) Cole-Hopf--Feynman-Kac formula and quasi-invariance of Navier-Stokes equations. Journal of Physics A: Mathematical and Theoretical, 50 (40). ISSN 1751-8113
Abstract
We make a refined comparison between the Navier–Stokes equations and their dynamically-scaled Leray equations solely on the basis of their scaling property. Previously it was observed using the vector potentials that they differ only by one drift term (Ohkitani 2017 J. Phys. A: Math. Theor. 50 045501). The Duhamel principle recasts the equations in path integral forms, which differ by two Maruyama–Girsanov densities. In this brief paper we simplify the concept of quasi-invariance (or, near-invariance) by combining the result with a Cole–Hopf transform and the Feynman–Kac formula. That way, as a multiplicative characterisation we can place those equations just one Maruyama–Girsanov density apart. Furthermore, as an additive characterisation we express the difference in terms of the Malliavin H-derivative.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IOP Publishing. This is an author produced version of a paper subsequently published in Journal of Physics A: Mathematical and Theoretical. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Navier-Stokes equations; Leray equations; dynamic scaling; critical spaces; Cameron-Martin-Maruyama-Girsanov theorem; Malliavin derivative; global regularity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/N022548/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Sep 2017 09:21 |
Last Modified: | 05 Sep 2018 00:38 |
Published Version: | https://doi.org/10.1088/1751-8121/aa841a |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/1751-8121/aa841a |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120929 |