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Pathwise Solutions of the 2-D Stochastic Primitive Equations

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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 (Ewald et al. in Anal. Appl. (Singap.) 5(2):183–198, 2007; Glatt-Holtz and Ziane in Discrete Contin. Dyn. Syst. Ser. B 10(4):801–822, 2008) 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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Authors and Affiliations

  1. Department of Mathematics and The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, USA

    Nathan Glatt-Holtz & Roger Temam

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  1. Nathan Glatt-Holtz
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  2. Roger Temam
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Correspondence to Nathan Glatt-Holtz.

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Dedicated to Alain Bensoussan on the occasion of his 70th birthday.

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Glatt-Holtz, N., Temam, R. Pathwise Solutions of the 2-D Stochastic Primitive Equations. Appl Math Optim 63, 401–433 (2011). https://doi.org/10.1007/s00245-010-9126-5

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