Year: 2014
Type: preprint
Abstract: We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This problem can be addressed within the framework of the recently developed theory of "regularity structures", which allows to describe candidate solutions locally by a "jet", but where the usual Taylor polynomials are replaced by a sequence of custom-built objects. In order to illustrate the theory, we focus on the particular example of the Kardar-Parisi-Zhang equation, a popular model for interface propagation.
Source: arXiv (Cornell University)
Author: Hairer, Martin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Leverhulme Trust
OpenAlex ID: W1572855569