Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise

被引:6
|
作者
Oh, Tadahiro [1 ,2 ]
Wang, Yuzhao [3 ]
Zine, Younes [1 ,2 ]
机构
[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland
[2] Maxwell Inst Math Sci, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland
[3] Univ Birmingham, Sch Math, Watson Bldg, Birmingham B15 2TT, W Midlands, England
来源
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2022年 / 10卷 / 03期
基金
欧洲研究理事会; 英国工程与自然科学研究理事会;
关键词
Stochastic nonlinear wave equation; Nonlinear wave equation; Pathwise well-posedness; GLOBAL WELL-POSEDNESS; SCHRODINGER-EQUATION; INVARIANT-MEASURES; GIBBS MEASURE; REGULARITY; EXISTENCE;
D O I
10.1007/s40072-022-00237-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on the three-dimensional torus T-3. In particular, we prove local well-posedness of the (renormalized) SNLW when the noise is almost a space-time white noise. In recent years, the paracontrolled calculus has played a crucial role in the well-posedness study of singular SNLW on T-3 by Gubinelli et al. (Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity, 2018, arXiv.1811.07808 [math.AP]), Oh et al. (Focusing Phi(4)(3)-model with a Hartree-type nonlinearity, 2020. arXiv:2009.03251 [math.PR]), and Bringmann (Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics, 2020, arXiv:2009.04616 [math.AP]). Our approach, however, does not rely on the paracontrolled calculus. We instead proceed with the second order expansion and study the resulting equation for the residual term, using multilinear dispersive smoothing.
引用
收藏
页码:898 / 963
页数:66
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