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Stochastic primitive equations with horizontal viscosity and diffusivity
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SYSNO ASEP 0575211 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Stochastic primitive equations with horizontal viscosity and diffusivity Author(s) Saal, M. (DE)
Slavík, Jakub (UTIA-B) ORCIDArticle number 54 Source Title Electronic Journal of Probability. - : Institute of Mathematical Statistics - ISSN 1083-6489
Roč. 28, č. 1 (2023)Number of pages 56 s. Publication form Online - E Language eng - English Country US - United States Keywords Horizontal viscosity ; Multiplicative noise ; Nonlinear stochastic PDE ; Primitive equations Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Open access Institutional support UTIA-B - RVO:67985556 UT WOS 000973790000006 EID SCOPUS 85156114913 DOI https://doi.org/10.1214/23-EJP940 Annotation We establish the existence and uniqueness of pathwise strong solutions to the stochastic 3D primitive equations with only horizontal viscosity and diffusivity driven by transport noise on a cylindrical domain M=(-h,0)xG, G⊂R^2 bounded and smooth, with the physical Dirichlet boundary conditions on the lateral part of the boundary. Compared to the deterministic case where the uniqueness of z-weak solutions holds in L^2, more regular initial data are necessary to establish uniqueness in the anisotropic space H^1_z L^2_{xy} so that the existence of local pathwise solutions can be deduced from the Gyöngy-Krylov theorem. Global existence is established using the logarithmic Sobolev embedding, the stochastic Gronwall lemma and an iterated stopping time argument. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2024 Electronic address https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Stochastic-primitive-equations-with-horizontal-viscosity-and-diffusivity/10.1214/23-EJP940.full
Number of the records: 1