Energy solutions of KPZ are unique

By Massimiliano Gubinelli, Nicolas Perkowski. 2015

144 citations recorded by the source corpus.

The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing that its energy solutions (as introduced by Gon\c{c}alves and Jara and later refined by Gubinelli and Jara) are unique. Together with various convergence results already present in the literature, this establishes the weak KPZ universality conjecture for a wide class of models. A remarkable consequence is that the energy solution to the KPZ equation is not equal to the Cole-Hopf solution, but it involves an additional drift $t/12$.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a564d9bc74c29d9453997cf5f50b2fea12b1fac7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The Dynamic $${\Phi^4_3}$$Φ34 Model Comes Down from Infinity (2016, methodology): “Related results were obtained for the KPZ equation, first in [2] via a Cole–Hopf transformation, and then, following [22], in a series of works including [11,17,19,20,27,29].”
Lectures on singular stochastic PDEs (2015, methodology): “were able to prove that energy solutions for the stationary stochastic Burgers equation are unique. This topic will not be touched upon here. The interested reader can ﬁnd the details in the preprint [GP15b]. 2.1 Distributions We will need to use distributions deﬁned on the d-dimensional torus Td wh”