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Singular stochastic PDEs

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arxiv 1403.6353 v1 pith:RR2GHQ2F submitted 2014-03-25 math.PR math.AP

Martin Hairer This is my paper · ORCID
classification math.PRmath.AP
keywords equationssingularstochastictheoryaddressedallowscandidatecustom-built
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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.

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Cited by 1 Pith paper

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  1. Nonlinear SPDEs and Maximal Regularity: An Extended Survey

    math.PR 2025-01 conditional novelty 4.0 of 10

    A survey with new extensions of the maximal-regularity framework for nonlinear SPDEs, yielding local well-posedness, blow-up criteria, and instantaneous regularization in critical spaces.

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