Generator functions and their applications

摘要

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]).