TY - JOUR
T1 - GENERATOR FUNCTIONS AND THEIR APPLICATIONS
AU - Grenier, Emmanuel
AU - Nguyen, Toan T.
N1 - Funding Information:
Received by the editors June 17, 2020, and, in revised form, February 7, 2021. 2020 Mathematics Subject Classification. Primary 35A10, 35A20, 35Q35, 35Q83. The second author’s research was partly supported by the NSF under grant DMS-1764119, an AMS Centennial fellowship, and a Simons fellowship.
Publisher Copyright:
© 2021 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0).
PY - 2021
Y1 - 2021
N2 - 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]).
AB - 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]).
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U2 - 10.1090/bproc/91
DO - 10.1090/bproc/91
M3 - Article
AN - SCOPUS:85120602732
SN - 2330-1511
VL - 8
SP - 245
EP - 251
JO - Proceedings of the American Mathematical Society, Series B
JF - Proceedings of the American Mathematical Society, Series B
ER -