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- Title
Hyperbolic Anderson Model 2: Strichartz Estimates and Stratonovich Setting.
- Authors
Chen, Xia; Deya, Aurélien; Song, Jian; Tindel, Samy
- 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.
- Subjects
ANDERSON model; BESOV spaces; WAVE equation; SPACETIME
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 21, p18575
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad039