We investigate a stochastic transport equation driven by a multiplicative noise. For drift coefficients in \(L^q(0,T;{\mathcal {C}}^\alpha _b({\mathbb {R}}^d))\) (\(\alpha >2/q\)) and initial data in \(W^{1,r}({\mathbb {R}}^d)\), we show the existence and uniqueness of stochastic strong solutions. Opposite to the deterministic case where the same assumptions on drift coefficients and initial data induce nonexistence of strong solutions, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. However, for \(\alpha +1<2/q\) with spatial dimension higher than one, we can choose suitable initial data and drift coefficients so that the stochastic strong solutions do not exist.

我们研究了由乘性噪声驱动的随机传输方程。对于\（L ^ q（0，T; {\ mathcal {C}} ^ \ alpha _b（{\ mathbb {R}} ^ d））\）（）中的漂移系数（\（\ alpha \ 2 / q \））和\（W ^ {1，r}（{\ mathbb {R}} ^ d）\）中的初始数据，我们证明了随机强解的存在性和唯一性。与对漂移系数和初始数据的相同假设导致不存在强解的确定性情况相反，我们证明布朗类型的乘性随机扰动足以使方程组成立。但是，对于空间尺寸大于1的\（\ alpha +1 <2 / q \），我们可以选择合适的初始数据和漂移系数，以便不存在随机强解。