论文标题
由Lévy噪声驱动的随机Strichartz估计值和随机非线性Schrödinger方程
The Stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise
论文作者
论文摘要
我们为由跳跃噪声驱动的随机卷积的随机strichartz估计值建立了新版本，我们将其应用于Marcus规范形式中的非线性乘数跳跃噪声。借助确定性的Strichartz估计值，我们证明了全球对随机非线性schrödinger方程在$ l^2（\ rr^n）$中的存在和唯一性，而在确定性的情况下，在整体临界范围内将注意力集中或偏向于非线性。
We establish a new version of the stochastic Strichartz estimate for the stochastic convolution driven by jump noise which we apply to the stochastic nonlinear Schrödinger equation with nonlinear multiplicative jump noise in the Marcus canonical form. With the help of the deterministic Strichartz estimates, we prove the existence and uniqueness of a global solution to stochastic nonlinear Schrödinger equation in $L^2(\RR^n)$ with either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case.
