TY - GEN
T1 - Invariant Measures in Coupled KPZ Equations
AU - Funaki, Tadahisa
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
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
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U2 - 10.1007/978-3-030-15096-9_20
DO - 10.1007/978-3-030-15096-9_20
M3 - Conference contribution
AN - SCOPUS:85069516514
SN - 9783030150952
T3 - Springer Proceedings in Mathematics and Statistics
SP - 560
EP - 568
BT - Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017
A2 - Giacomin, Giambattista
A2 - Olla, Stefano
A2 - Saada, Ellen
A2 - Spohn, Herbert
A2 - Stoltz, Gabriel
A2 - Stoltz, Gabriel
PB - Springer New York LLC
T2 - International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017
Y2 - 12 June 2017 through 16 June 2017
ER -