论文标题
$ ϕ^4 $的不变性在飞机上的非线性波和schrödinger方程下的不变性
Invariance of $ϕ^4$ measure under nonlinear wave and Schrödinger equations on the plane
论文作者
论文摘要
我们在$ \ Mathbb r^2 $上的加权空间中显示了较大的BESOV空间中的较大的立方波动方程的概率存在和唯一性。为了实现这一目标，我们表明，在等式下，$ ϕ^4 $度量的弱极限是不变的。我们审查并稍微简化了弱极限量度的周期理论和构建，然后使用有限的传播速度将无限体积案例减少到先前的设置。我们的论点还使在同一环境中的非线性schrödinger方程导致弱（Albeverio-cruzeiro）不变性。
We show probabilistic existence and uniqueness for the Wick-ordered cubic nonlinear wave equation in a weighted Besov space over $\mathbb R^2$. To achieve this, we show that a weak limit of $ϕ^4$ measures on increasing tori is invariant under the equation. We review and slightly simplify the periodic theory and the construction of the weak limit measure, and then use finite speed of propagation to reduce the infinite-volume case to the previous setup. Our argument also gives a weak (Albeverio--Cruzeiro) invariance result on the nonlinear Schrödinger equation in the same setting.
