论文标题
双眼安德森(Anderson)型号2:Strichartz估计和Stratonovich设置
Hyperbolic Anderson model 2: Strichartz estimates and Stratonovich setting
论文作者
论文摘要
我们在\ {1,2 \} $中以乘以时空高斯噪声研究了dimension $ d \中的波方程。 Stratonovich溶液的存在和独特性是在施加在高斯噪声上的某些条件下获得的。该策略是为加权空间中的波核开发一些strichartz类型估计,我们可以证明相关的年轻型方程的良好性。那些Strichartz的界限具有独立的利益。
We study a wave equation in dimension $d\in \{1,2\}$ with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on the Gaussian noise. The strategy is to develop some Strichartz type estimates for the wave kernel in weighted Besov spaces, by which we can prove the wellposedness of an associated Young-type equation. Those Strichartz bounds are of independent interest.