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Hyperbolic Anderson Model 2: Strichartz Estimates and Stratonovich Setting.

Authors :
Chen, Xia
Deya, Aurélien
Song, Jian
Tindel, Samy
Source :
IMRN: International Mathematics Research Notices. Nov2023, Vol. 2023 Issue 21, p18575-18628. 54p.
Publication Year :
2023

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10737928
Volume :
2023
Issue :
21
Database :
Academic Search Index
Journal :
IMRN: International Mathematics Research Notices
Publication Type :
Academic Journal
Accession number :
173587614
Full Text :
https://doi.org/10.1093/imrn/rnad039