论文标题
随机噪声强制强迫运输扩散方程法的非唯一性
Non-uniqueness in law of transport-diffusion equation forced by random noise
论文作者
论文摘要
我们考虑由三种类型的随机噪声强制强制的传输扩散方程：加法，线性乘法$ \ hat {\ mathrm {o}} $的解释以及Stratonovich的解释中的传输。通过凸集成，通过概率设置修改，我们证明了sobolev空间中具有空间规律性的无差异矢量场的存在，并相应地解决了列布斯格空间中的空间规律性的传输扩散方程，因此在法律中无唯一性在法律中，在全球范围内全球范围的法律级别。
We consider a transport-diffusion equation forced by random noise of three types: additive, linear multiplicative in It$\hat{\mathrm{o}}$'s interpretation, and transport in Stratonovich's interpretation. Via convex integration modified to probabilistic setting, we prove existence of a divergence-free vector field with spatial regularity in Sobolev space and corresponding solution to a transport-diffusion equation with spatial regularity in Lebesgue space, and consequently non-uniqueness in law at the level of probabilistically strong solutions globally in time.
