Invariant Measures in Coupled KPZ Equations

Tadahisa Funaki*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


We discuss coupled KPZ (Kardar-Parisi-Zhang) equations. The motivation comes from the study of nonlinear fluctuating hydrodynamics, cf. [11, 12]. We first give a quick overview of results of Funaki and Hoshino [6], in particular, two approximating equations, trilinear condition (T) for coupling constants Γ, invariant measures and global-in-time existence of solutions. Then, we study at heuristic level the role of the trilinear condition (T) in view of invariant measures and renormalizations for 4th order terms. Ertaş and Kardar [2] gave an example which does not satisfy (T) but has an invariant measure. We finally discuss the cross-diffusion case.

Original languageEnglish
Title of host publicationStochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017
EditorsGiambattista Giacomin, Stefano Olla, Ellen Saada, Herbert Spohn, Gabriel Stoltz, Gabriel Stoltz
PublisherSpringer New York LLC
Number of pages9
ISBN (Print)9783030150952
Publication statusPublished - 2019
EventInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017 - Paris, France
Duration: 2017 Jun 122017 Jun 16

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


ConferenceInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017


  • Coupled KPZ equation
  • Invariant measure
  • Renormalization
  • Trilinear condition

ASJC Scopus subject areas

  • Mathematics(all)


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