Hyperbolic Anderson Model 2: Strichartz Estimates and Stratonovich Setting

被引：0

作者：

Chen, Xia ^{[1
]}

Deya, Aurelien ^{[2
]}

Song, Jian ^{[3
]}

Tindel, Samy ^{[4
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Univ Lorraine, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, Lorraine, France

[3] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Shandong, Peoples R China

[4] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 21期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

WAVE-EQUATION;

D O I：

10.1093/imrn/rnad039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a wave equation in dimension $d\in \{1,2\}$ with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on the Gaussian noise. The strategy is to develop some Strichartz-type estimates for the wave kernel in weighted Besov spaces, by which we can prove the well-posedness of an associated Young-type equation. Those Strichartz bounds are of independent interest.

引用

页码：18575 / 18628

页数：54