RENORMALIZATION OF THE TWO-DIMENSIONAL STOCHASTIC NONLINEAR WAVE EQUATIONS

被引：53

作者：

Gubinelli, Massimiliano ^{[1
,2
]}

Koch, Herbert ^{[3
]}

Oh, Tadahiro ^{[4
,5
]}

机构：

[1] Univ Bonn, Hausdorff Ctr Math, Endenicher Allee 60, D-53115 Bonn, Germany

[2] Univ Bonn, Inst Angewandte Math, Endenicher Allee 60, D-53115 Bonn, Germany

[3] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

[4] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

[5] Maxwell Inst Math Sci, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 10期

基金：

欧洲研究理事会;

关键词：

Stochastic nonlinear wave equation; nonlinear wave equation; renormalization; Wick ordering; Hermite polynomial; white noise;

D O I：

10.1090/tran/7452

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renormalization and prove that SNLW is pathwise locally well-posed. As an application of the local well-posedness argument, we also establish a weak universality result for the renormalized SNLW.

引用

页码：7335 / 7359

页数：25

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