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

Fingerprint

Invariant Measure
Fluctuating Hydrodynamics
Cross-diffusion
Renormalization
Existence of Solutions
Heuristics
Term

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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

Invariant Measures in Coupled KPZ Equations. / Funaki, Tadahisa.

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

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

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. 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
Funaki T. Invariant Measures in Coupled KPZ Equations. In Stoltz G, Spohn H, Giacomin G, Olla S, Stoltz G, Saada E, editors, Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017. Springer New York LLC. 2019. p. 560-568. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-030-15096-9_20
Funaki, Tadahisa. / Invariant Measures in Coupled KPZ Equations. Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017. editor / Gabriel Stoltz ; Herbert Spohn ; Giambattista Giacomin ; Stefano Olla ; Gabriel Stoltz ; Ellen Saada. Springer New York LLC, 2019. pp. 560-568 (Springer Proceedings in Mathematics and Statistics).
@inproceedings{d1eef92a21954fc6b3c7bfb242f641a5,
title = "Invariant Measures in Coupled KPZ Equations",
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.",
keywords = "Coupled KPZ equation, Invariant measure, Renormalization, Trilinear condition",
author = "Tadahisa Funaki",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-3-030-15096-9_20",
language = "English",
isbn = "9783030150952",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "560--568",
editor = "Gabriel Stoltz and Herbert Spohn and Giambattista Giacomin and Stefano Olla and Gabriel Stoltz and Ellen Saada",
booktitle = "Stochastic Dynamics Out of Equilibrium - Institut Henri Poincar{\'e}, 2017",

}

TY - GEN

T1 - Invariant Measures in Coupled KPZ Equations

AU - Funaki, Tadahisa

PY - 2019/1/1

Y1 - 2019/1/1

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.

AB - 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.

KW - Coupled KPZ equation

KW - Invariant measure

KW - Renormalization

KW - Trilinear condition

UR - http://www.scopus.com/inward/record.url?scp=85069516514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069516514&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-15096-9_20

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

M3 - Conference contribution

SN - 9783030150952

T3 - Springer Proceedings in Mathematics and Statistics

SP - 560

EP - 568

BT - Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017

A2 - Stoltz, Gabriel

A2 - Spohn, Herbert

A2 - Giacomin, Giambattista

A2 - Olla, Stefano

A2 - Stoltz, Gabriel

A2 - Saada, Ellen

PB - Springer New York LLC

ER -