0575211 20240402214355.020230906235959.9 85156114913 000973790000006 10.1214/23-EJP940 56 s. E cav_un_epca*00419541083-648928Institute of Mathematical Statistics Horizontal viscosity Multiplicative noise Nonlinear stochastic PDE Primitive equations cav_un_auth*0455071 Saal M. DE cav_un_auth*0370372 Slavík Jakub UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics CZ Ústav teorie informace a automatizace AV ČR, v. v. i. 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 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. WOS BA 10000 10100 10101 2024 RVO:67985556 https://hdl.handle.net/11104/0345388 S 54 Article Statistics Probability A STATISTICS&PROBABILITY 1.3 0.2 7.8 0.00769 1.288 2436 55 1.419 35.47 1.2 580 Q1 1.200 166 Q2 61.6 Q2 Q1 0.59 Q2 61.6 2023 85156114913 SCOPUS PUBMED 000973790000006 WOS cav_un_epca*0041954 Electronic Journal of Probability Roč. 28 1 2023 1083-6489 1083-6489 Institute of Mathematical Statistics