0575211 - ÚTIA 2024 RIV US eng J - Journal Article
Saal, M. - Slavík, Jakub
Stochastic primitive equations with horizontal viscosity and diffusivity.
Electronic Journal of Probability. Roč. 28, č. 1 (2023), č. článku 54. ISSN 1083-6489. E-ISSN 1083-6489
Institutional support: RVO:67985556
Keywords : Horizontal viscosity * Multiplicative noise * Nonlinear stochastic PDE * Primitive equations
OECD category: Pure mathematics
Impact factor: 1.3, year: 2023 ; AIS: 1.288, rok: 2023
Method of publishing: Open access
Result website:
http://library.utia.cas.cz/separaty/2023/SI/slavik-0575211.pdf 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

DOI: https://doi.org/10.1214/23-EJP940

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.
Permanent Link: https://hdl.handle.net/11104/0345388