Hyperbolic Anderson Model 2: Strichartz Estimates and Stratonovich Setting-Reference-Cited by-同舟云学术

Hyperbolic Anderson Model 2: Strichartz Estimates and Stratonovich Setting

Published:2023-04-04 Issue:21 Volume:2023 Page:18575-18628
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Chen Xia¹,Deya Aurélien²,Song Jian³,Tindel Samy⁴

Affiliation:

1. Department of Mathematics , University of Tennessee, Knoxville, TN 37996-1320, USA

2. Institut Elie Cartan , University of Lorraine, Vandoeuvre-l {\`e} s-Nancy, Lorraine 54506, France

3. Research Center for Mathematics and Interdisciplinary Sciences , Shandong University, Qingdao, Shandong 266237, China

4. Department of Mathematics , Purdue UniversityWest Lafayette, IN 47907-2067, USA

Abstract

Abstract 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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2023/21/18575/52944552/rnad039.pdf

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