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

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 Ĥ 1 p , p 2 (R) (4 ≤ p < ∞) with rough data. In particular, we show that s ≥ 1 p is the necessary condition for the maximal function estimate in Ĥ s , p 2 (R) , which means that s = 1 p is optimal for rough data. On the other hand, we present the stochastic continuity of free reduced Ostrovsky equation at t = 0 in Fourier–Lebesgue spaces L ̂ r (R) (2 ≤ r < ∞) with random data. [ABSTRACT FROM AUTHOR]