Generator functions and their applications
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- by Emmanuel Grenier and Toan T. Nguyen HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 8 (2021), 245-251
Abstract:
We had introduced so called generators functions to precisely follow the regularity of analytic solutions of Navier-Stokes equations earlier (see Grenier and Nguyen [Ann. PDE 5 (2019)]. In this short note, we give a short presentation of these generator functions and use them to construct analytic solutions to classical evolution equations, which provides an alternative way to the use of the classical abstract Cauchy-Kovalevskaya theorem (see Asano [Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), pp. 102–105], Baouendi and Goulaouic [Comm. Partial Differential Equations 2 (1977), pp. 1151–1162], Caflisch [Bull. Amer. Math. Soc. (N.S.) 23 (1990), pp. 495–500], Nirenberg [J. Differential Geom. 6 (1972), pp. 561–576], Safonov [Comm. Pure Appl. Math. 48 (1995), pp. 629–637]).References
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Additional Information
- Emmanuel Grenier
- Affiliation: Equipe Projet Inria NUMED, INRIA Rhône Alpes, Unité de Mathématiques Pures et Appliquées., UMR 5669, CNRS et École Normale Supérieure de Lyon, 46, allée d’Italie, 69364 Lyon Cedex 07, France
- MR Author ID: 346619
- Email: emmanuel.Grenier@ens-lyon.fr
- Toan T. Nguyen
- Affiliation: Department of Mathematics, Penn State University, State College, Pennsylvania 16803
- MR Author ID: 718370
- Email: nguyen@math.psu.edu
- Received by editor(s): June 17, 2020
- Received by editor(s) in revised form: February 7, 2021
- Published electronically: August 19, 2021
- Additional Notes: The second author’s research was partly supported by the NSF under grant DMS-1764119, an AMS Centennial fellowship, and a Simons fellowship.
- Communicated by: Catherine Sulem
- © Copyright 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 8 (2021), 245-251
- MSC (2020): Primary 35A10, 35A20, 35Q35, 35Q83
- DOI: https://doi.org/10.1090/bproc/91
- MathSciNet review: 4302152