Global Solutions to Elliptic and Parabolic $${\Phi^4}$$Φ4 Models in Euclidean Space
Global Solutions to Elliptic and Parabolic $${\Phi^4}$$Φ4 Models in Euclidean Space
复制标题
欧几里德空间中椭圆和抛物线 $${Phi^4}$$Φ4 模型的全局解
DOI：
10.1007/s00220-019-03398-4
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发表时间：
2018
影响因子：
2.4
通讯作者：
M. Hofmanová
中科院分区：
文献类型：
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作者：
M. Gubinelli;M. Hofmanová
我们证明了整体解的存在性奇异SPDE $${\mathbb{R}^{\rm d}}$$Rd立方非线性和添加剂白色噪声扰动，无论是在椭圆设置的尺寸d = 4，5和在抛物设置d = 2，3。我们证明了抛物型方程的唯一性和从无穷远下降。考虑这些方程的一个动机是标量相互作用欧几里德量子场论的构建。抛物型方程通过Parisi-Wu随机量子化与$${\Phi^{4}_d}$$Φ d-4欧几里德量子场论相联系，而椭圆型方程通过Parisi-Sourlas降维机制与$${\Phi^{4}_d-2}}$$Φd-24欧几里德量子场论相联系.
We prove the existence of global solutions to singular SPDEs on $${\mathbb{R}^{\rm d}}$$Rd with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions d = 4, 5 and in the parabolic setting for d = 2, 3. We prove uniqueness and coming down from infinity for the parabolic equations. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the $${\Phi^{4}_d}$$Φd4 Euclidean quantum field theory via Parisi–Wu stochastic quantization, while the elliptic equations are linked to the $${\Phi^{4}_{d-2}}$$Φd-24 Euclidean quantum field theory via the Parisi–Sourlas dimensional reduction mechanism.