Lvy噪声驱动的随机b族方程的适定性

Well-posedness for stochastic b-family equation with Lvy noise

本文考虑Lvy噪声驱动的随机b族方程的适定性.首先,由压缩映射原理得到随机黏性b族方程的局部适定性.接着,由正则化方法,得到一个Cauchy列,其相应的极限为随机b族方程的唯一解.

In this paper, the stochastic b-family equation with Levy noise is considered. Firstly, the local well- posedness for the stochastic viscous b-family equation is established by the contracting mapping principle. Then, by the regularization method, a Cauchy sequence is obtained, from which the well-posedness of the stochastic b-family equation is proved.