Invariant Measures in Coupled KPZ Equations

Tadahisa Funaki

doi:10.1007/978-3-030-15096-9_20

Invariant Measures in Coupled KPZ Equations

Tadahisa Funaki^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

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 language	English
Title of host publication	Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017
Editors	Giambattista Giacomin, Stefano Olla, Ellen Saada, Herbert Spohn, Gabriel Stoltz, Gabriel Stoltz
Publisher	Springer New York LLC
Pages	560-568
Number of pages	9
ISBN (Print)	9783030150952
DOIs	https://doi.org/10.1007/978-3-030-15096-9_20
Publication status	Published - 2019
Event	International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017 - Paris, France Duration: 2017 Jun 12 → 2017 Jun 16

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	282
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017
Country/Territory	France
City	Paris
Period	17/6/12 → 17/6/16

Keywords

Coupled KPZ equation
Invariant measure
Renormalization
Trilinear condition

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-3-030-15096-9_20

Cite this

Invariant Measures in Coupled KPZ Equations. / Funaki, Tadahisa.
Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017. ed. / Giambattista Giacomin; Stefano Olla; Ellen Saada; Herbert Spohn; Gabriel Stoltz; Gabriel Stoltz. Springer New York LLC, 2019. p. 560-568 (Springer Proceedings in Mathematics and Statistics; Vol. 282).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Funaki, T 2019, Invariant Measures in Coupled KPZ Equations. in G Giacomin, S Olla, E Saada, H Spohn, G Stoltz & G Stoltz (eds), Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017. Springer Proceedings in Mathematics and Statistics, vol. 282, Springer New York LLC, pp. 560-568, International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017, Paris, France, 17/6/12. https://doi.org/10.1007/978-3-030-15096-9_20

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keywords = "Coupled KPZ equation, Invariant measure, Renormalization, Trilinear condition",

author = "Tadahisa Funaki",

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N2 - 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.

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Invariant Measures in Coupled KPZ Equations

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