Ergodicity of stochastic damped Ostrovsky equation driven by white noise
The paper is concerned with the stochastic so-called damped Ostrovsky equation. The deterministic counterpart of the equation studied in the paper was proposed by \textit{L. Ostrovsky} [``Nonlinear internal waves in a rotating ocean'', Okeanolog. 18, 181--191 (1978)] as a model for weakly nonlinear waves in a rotating liquid. The equation describes the propagation of surface waves in the ocean in a rotating frame of reference. In the article, the global existence of the mild solution to the stochastic damped Ostrovsky equation with random initial value is proved. Moreover, the existence of invariant measure with random initial value and ergodic invariant measure with deterministic initial condition are given. The article is a continuation of works concerning the Ostrovsky equation written by some of paper's authors [NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 3, Paper No. 22, 37 p. (2018; Zbl 1394.35380); J. Differ. Equations 267, No. 10, 5701--5735 (2019; Zbl 1420.35483)]. It can be interesting for people working in this field. Reviewer's remark: I regret to say that the paper is poorly written and looks like printed without any proof correction. I am astonished by the number of errors of several kinds: language, punctuation, improper use of one reference, lack of explanation of some notations, etc. I found more than 60 such errors. Most of them are minor shortcomings, but their number is unexpected for such a reputable journal as Discrete and Continuous Dynamical Systems.
scientific article; zbMATH DE number 7355163
scientific article