A coupled KPZ equation, its two types of approximations and existence of global solutions

Tadahisa Funaki, Masato Hoshino

研究成果: ジャーナルへの寄稿記事

10 引用 (Scopus)

抄録

This paper concerns the multi-component coupled Kardar–Parisi–Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper renormalization, while the other one introduced in [6] is suitable for studying the invariant measures. By applying the paracontrolled calculus introduced by Gubinelli et al. [8,9], we show that two approximations have the common limit under the properly adjusted choice of renormalization factors for each of these approximations. In particular, if the coupling constants of the nonlinear term of the coupled KPZ equation satisfy the so-called “trilinear” condition, the renormalization factors can be taken the same in two approximations and the difference of the limits of two approximations are explicitly computed. Moreover, under the trilinear condition, the Wiener measure twisted by the diffusion matrix becomes stationary for the limit and we show that the solution of the limit equation exists globally in time when the initial value is sampled from the stationary measure. This is shown for the associated tilt process. Combined with the strong Feller property shown by Hairer and Mattingly [12], this result can be extended for all initial values.

元の言語英語
ページ(範囲)1165-1204
ページ数40
ジャーナルJournal of Functional Analysis
273
発行部数3
DOI
出版物ステータス出版済み - 8 1 2017

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Global Solution
Approximation
Renormalization
Strong Feller Property
Wiener Measure
Stationary Measure
Term
Tilt
Invariant Measure
Replacement
Calculus

All Science Journal Classification (ASJC) codes

  • Analysis

これを引用

A coupled KPZ equation, its two types of approximations and existence of global solutions. / Funaki, Tadahisa; Hoshino, Masato.

:: Journal of Functional Analysis, 巻 273, 番号 3, 01.08.2017, p. 1165-1204.

研究成果: ジャーナルへの寄稿記事

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