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arXiv 1301.40122013-01-17math.APmath.PR

具有Hölder漂移的随机迁移方程的注记

Remarks on the stochastic transport equation with Hölder drift

Franco Flandoli, Massimiliano Gubinelli, Enrico Priola

备注：: arXiv admin note: text overlap with arXiv:0809.1310

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摘要：

考虑一类随机线性迁移方程，其向量场是全局Hölder连续有界的.与可能出现冲击的确定性情形相反，我们证明了以C^{1}-初始条件开始的唯一解在空间中仍然是$C^{1}$类。我们还改进了Flandoli-Gubinelli-Priola（2009）关于适定性的一些结果.此外，我们证明了一个稳定性的了解关于初始数据。

英文摘要：

We consider a stochastic linear transport equation with a globally Hölder continuous and bounded vector field. Opposite to what happens in the deterministic case where shocks may appear, we show that the unique solution starting with a C^{1}-initial condition remains of class $C^{1}$ in space. We also improve some results of Flandoli-Gubinelli-Priola (2009) about well-posedness. Moreover, we prove a stability property for the solution with respect to the initial datum.

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