Errata to “Energetic variational approaches for incompressible fluid systems on an evolving surface”
Authors:
Hajime Koba, Chun Liu and Yoshikazu Giga
Journal:
Quart. Appl. Math. 76 (2018), 147-152
MSC (2010):
Primary 49S05, 49Q20
DOI:
https://doi.org/10.1090/qam/1482
Published electronically:
September 28, 2017
Original Article:
Quart. Appl. Math. 75 (2017), 359-389.
MathSciNet review:
3733097
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Additional Information
Abstract: There are two minor flaws in our 2017 paper. The first flaw is in the proof of Lemma 2.7, which relates a generalization of Helmholtz-Weyl decomposition on a closed surface. The second one is in Appendix (I), where we compare our model to Taylor’s model when the surface does not move. We give a full proof of Lemma 2.7 as well as a correct comparison of our model with Taylor’s model (1992). It will be properly interpreted.
References
- Marc Arnaudon and Ana Bela Cruzeiro, Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability, Bull. Sci. Math. 136 (2012), no. 8, 857–881. MR 2995006, DOI https://doi.org/10.1016/j.bulsci.2012.06.007
- Thierry Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 252, Springer-Verlag, New York, 1982. MR 681859
- Thomas Jankuhn, Maxim A. Olshanskii, and Arnold Reusken, Incompressible fluid problems on embedded surfaces: modeling and variational formulations. preprint. Arxiv: 1702.02989v1
- Jürgen Jost, Riemannian geometry and geometric analysis, 6th ed., Universitext, Springer, Heidelberg, 2011. MR 2829653
- Hajime Koba, On derivation of incompressible fluid systems with heat equation", to appear in S$\hat {u}$rikaisekikenky$\hat {u}$sho K$\hat {o}$ky$\hat {u}$roku (Mathematical Analysis of Viscous Incompressible Fluid (Kyoto, 2016)).
- Hajime Koba, Chun Liu, and Yoshikazu Giga, Energetic variational approaches for incompressible fluid systems on an evolving surface, Quart. Appl. Math. 75 (2017), no. 2, 359–389. MR 3614501, DOI https://doi.org/10.1090/qam/1452
- Yoshihiko Mitsumatsu and Yasuhisa Yano, Geometry of an incompressible fluid on a Riemannian manifold, Sūrikaisekikenkyūsho K\B{o}kyūroku 1260 (2002), 33–47 (Japanese). Geometric mechanics (Japanese) (Kyoto, 2002). MR 1930362
- Tatsu-Hiko Miura, On singular limit equations for incompressible fluids in moving thin domains, preprint. Arxiv: 1703.09698v1
- Michael E. Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Comm. Partial Differential Equations 17 (1992), no. 9-10, 1407–1456. MR 1187618, DOI https://doi.org/10.1080/03605309208820892
References
- Marc Arnaudon and Ana Bela Cruzeiro, Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability, Bull. Sci. Math. 136 (2012), no. 8, 857–881. MR 2995006, DOI https://doi.org/10.1016/j.bulsci.2012.06.007
- Thierry Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 252, Springer-Verlag, New York, 1982. MR 681859
- Thomas Jankuhn, Maxim A. Olshanskii, and Arnold Reusken, Incompressible fluid problems on embedded surfaces: modeling and variational formulations. preprint. Arxiv: 1702.02989v1
- Jürgen Jost, Riemannian geometry and geometric analysis, 6th ed., Universitext, Springer, Heidelberg, 2011. MR 2829653
- Hajime Koba, On derivation of incompressible fluid systems with heat equation", to appear in S$\hat {u}$rikaisekikenky$\hat {u}$sho K$\hat {o}$ky$\hat {u}$roku (Mathematical Analysis of Viscous Incompressible Fluid (Kyoto, 2016)).
- Hajime Koba, Chun Liu, and Yoshikazu Giga, Energetic variational approaches for incompressible fluid systems on an evolving surface, Quart. Appl. Math. 75 (2017), no. 2, 359–389. MR 3614501, DOI https://doi.org/10.1090/qam/1452
- Yoshihiko Mitsumatsu and Yasuhisa Yano, Geometry of an incompressible fluid on a Riemannian manifold, Sūrikaisekikenkyūsho Kōkyūroku 1260 (2002), 33–47 (Japanese). Geometric mechanics (Japanese) (Kyoto, 2002). MR 1930362
- Tatsu-Hiko Miura, On singular limit equations for incompressible fluids in moving thin domains, preprint. Arxiv: 1703.09698v1
- Michael E. Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Comm. Partial Differential Equations 17 (1992), no. 9-10, 1407–1456. MR 1187618, DOI https://doi.org/10.1080/03605309208820892
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Additional Information
Hajime Koba
Affiliation:
Graduate School of Engineering Science, Osaka University,, 1-3 Machikaneyamacho, Toyonaka, Osaka, 560-8531, Japan
MR Author ID:
1013948
Email:
iti@sigmath.es.osaka-u.ac.jp
Chun Liu
Affiliation:
Department of Mathematics, Penn State University,, 107A McAllister Building, University Park, PA 16802
Address at time of publication:
Department of Applied Mathematics, Illinois Institute of Technology, Rettaliata Engineering Center, 10 W. 32nd St., Room 208, Chicago, IL 60616
MR Author ID:
362496
ORCID:
[object Object]
Email:
liuc@psu.edu; cliu124@iit.edu
Yoshikazu Giga
Affiliation:
Department of Mathematical Sciences, University of Tokyo,, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan.
MR Author ID:
191842
Email:
labgiga@ms.u-tokyo.ac.jp
Received by editor(s):
June 8, 2017
Published electronically:
September 28, 2017
Additional Notes:
The work of the first author was partly supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP25887048 and JP15K17580.
The work of the second author was partially supported by National Science Foundation grants DMS-1412005, DMS-1216938, and DMS-1159937.
The work of the third author was partly supported by JSPS through the grants Kiban S number 26220702, Kiban A number 23244015 and Houga number 25610025.
Article copyright:
© Copyright 2017
Brown University
