Pathwise Solutions of the 2D Stochastic Primitive Equations

2010/07/16 by Nathan Glatt-Holtz, Roger Témam, Glatt-Holtz, Nathan +1
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · #35Q35 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Meteorological Phenomena and Simulations #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1007.2833

openalex publication_date 2010/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we consider a stochastic version of the Primitive Equations (PEs) of the ocean and the atmosphere and establish the existence and uniqueness of pathwise, strong solutions. The analysis employs novel techniques in contrast to previous works in order to handle a general class of nonlinear noise structures and to allow for physically relevant boundary conditions. The proof relies on Cauchy estimates, stopping time arguments and anisotropic estimates.

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