article published yes Antonio Agresti author 673cd0cc-9b9a-11eb-b144-88f30e1fbb720000-0002-9573-2962 Matthias Hieber author Amru Hussein author Martin Saal author JuFi department In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well. https://research-explorer.ista.ac.at/download/12178/17297/2024_StochasticsEquations_Agresti.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Springer Nature2024 eng Applied MathematicsModeling and SimulationStatistics and Probability 2194-0401 2194-041X 2109.09561 00087438900000110.1007/s40072-022-00277-3 1253-133 Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 12, Springer Nature, 2024, pp. 53–133, doi:<a href="https://doi.org/10.1007/s40072-022-00277-3">10.1007/s40072-022-00277-3</a>. A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024) 53–133. Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2024). The stochastic primitive equations with transport noise and turbulent pressure. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href="https://doi.org/10.1007/s40072-022-00277-3">https://doi.org/10.1007/s40072-022-00277-3</a> Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s40072-022-00277-3">https://doi.org/10.1007/s40072-022-00277-3</a>. Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with transport noise and turbulent pressure. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2024;12:53-133. doi:<a href="https://doi.org/10.1007/s40072-022-00277-3">10.1007/s40072-022-00277-3</a> A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with transport noise and turbulent pressure,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 12. Springer Nature, pp. 53–133, 2024. Agresti A, Hieber M, Hussein A, Saal M. 2024. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations. 12, 53–133. 121782023-01-12T12:12:29Z2024-07-22T09:30:40Z