Convergence problem of reduced Ostrovsky equation in Fourier–Lebesgue spaces with rough data and random data

Abstract

This paper is devoted to studying the convergence problem of free reduced Ostrovsky equation in Fourier–Lebesgue spaces with rough data and the stochastic continuity of free reduced Ostrovsky equation in Fourier–Lebesgue spaces with random data. On the one hand, we establish the pointwise convergence related to the free reduced Ostrovsky equation in Fourier–Lebesgue spaces [Formula: see text] with rough data. In particular, we show that [Formula: see text] is the necessary condition for the maximal function estimate in [Formula: see text], which means that [Formula: see text] is optimal for rough data. On the other hand, we present the stochastic continuity of free reduced Ostrovsky equation at [Formula: see text] in Fourier–Lebesgue spaces [Formula: see text] with random data.