Invariant Measures in Coupled KPZ Equations

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

Abstract

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
EditorsGabriel Stoltz, Herbert Spohn, Giambattista Giacomin, Stefano Olla, Gabriel Stoltz, Ellen Saada
PublisherSpringer New York LLC
Pages560-568
Number of pages9
ISBN (Print)9783030150952
DOIs
Publication statusPublished - 2019 Jan 1
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
Volume282
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017
CountryFrance
CityParis
Period17/6/1217/6/16

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Funaki, T. (2019). Invariant Measures in Coupled KPZ Equations. In G. Stoltz, H. Spohn, G. Giacomin, S. Olla, G. Stoltz, & E. Saada (Eds.), Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017 (pp. 560-568). (Springer Proceedings in Mathematics and Statistics; Vol. 282). Springer New York LLC. https://doi.org/10.1007/978-3-030-15096-9_20