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]).

UR - http://www.scopus.com/inward/record.url?scp=85120602732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85120602732&partnerID=8YFLogxK

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 -