The current paper is devoted to the stochastic damped Ostrovsky equation driven by white noise. By establishing the uniform estimates for the solution in $ H^1 $ norm, we prove the global well-posedness and the existence of invariant measure for stochastic damped Ostrovsky equation with random initial value. Moreover, we obtain the ergodicity of stochastic damped Ostrovsky equation with deterministic initial conditions.

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白噪声驱动的随机阻尼Ostrovsky方程的遍历性

本文致力于白噪声驱动的随机阻尼Ostrovsky方程。通过建立在$ H ^ 1 $范数下的统一解估计，我们证明了具有随机初始值的随机阻尼Ostrovsky方程的整体适定性和不变测度的存在。此外，我们获得了具有确定性初始条件的随机阻尼Ostrovsky方程的遍历性。