论文标题
一类非线性波方程的普遍性结果
Weak universality results for a class of nonlinear wave equations
论文作者
论文摘要
我们研究了二维分数非线性波方程的弱普遍性。对于一系列具有高度电势的汉密尔顿人，将缩放为分数$φ_2^4 $，我们首先建立了一个\ emph {足够且几乎必要的}标准，以使不变度度量与分数$φ_2^4 $融合。然后，我们证明了相关波动力学序列与（重新归一化的）立方波方程的收敛结果。我们对分数指数的限制与非线性程度无关。这扩展了Gubinelli-Koch-OH的结果[二维随机非线性波方程的重新分解，trans。阿米尔。数学。 Soc。 370（2018）]在我们没有具有高批评性非线性的本地库奇理论的情况下。
We study the weak universality of the two-dimensional fractional nonlinear wave equation. For a sequence of Hamiltonians of high-degree potentials scaling to the fractional $Φ_2^4$, we first establish a \emph{sufficient and almost necessary} criteria for the convergence of invariant measures to the fractional $Φ_2^4$. Then we prove the convergence result for the sequence of associated wave dynamics to the (renormalized) cubic wave equation. Our constraint on the fractional index is independent of the degree of the nonlinearity. This extends the result of Gubinelli-Koch-Oh [Renormalisation of the two-dimensional stochastic nonlinear wave equations, Trans. Amer. Math. Soc. 370 (2018)] to a situation where we do not have a local Cauchy theory with highly supercritical nonlinearities.
