American Institute of Mathematical Sciences

Advanced
September  2008, 10(4): 801-822. doi: 10.3934/dcdsb.2008.10.801

The stochastic primitive equations in two space dimensions with multiplicative noise

Nathan Glatt-Holtz 1, and  Mohammed Ziane 1,

1. 

Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States, United States

Received  August 2007 Revised  March 2008 Published  August 2008

We study the two dimensional primitive equations in the presence of multiplicative stochastic forcing. We prove the existence and uniqueness of solutions in a fixed probability space. The proof is based on finite dimensional approximations, anisotropic Sobolev estimates, and weak convergence methods.
Keywords: Stochastic Partial Differential Equations, Primitive Equations, Existence and Uniqueness., Galerkin Approximation, Geophysical Fluid Dynamics.
Mathematics Subject Classification: Primary: 76D03, 60H15; Secondary: 37L6.
Citation: Nathan Glatt-Holtz, Mohammed Ziane. The stochastic primitive equations in two space dimensions with multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 801-822. doi: 10.3934/dcdsb.2008.10.801
[1]

Jeffrey J. Early, Juha Pohjanpelto, Roger M. Samelson. Group foliation of equations in geophysical fluid dynamics. Discrete & Continuous Dynamical Systems, 2010, 27 (4) : 1571-1586. doi: 10.3934/dcds.2010.27.1571
[2]

Qi Yao, Linshan Wang, Yangfan Wang. Existence-uniqueness and stability of the mild periodic solutions to a class of delayed stochastic partial differential equations and its applications. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4727-4743. doi: 10.3934/dcdsb.2020310
[3]

Boling Guo, Guoli Zhou. On the backward uniqueness of the stochastic primitive equations with additive noise. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3157-3174. doi: 10.3934/dcdsb.2018305
[4]

T. Tachim Medjo. Existence and uniqueness of strong periodic solutions of the primitive equations of the ocean. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1491-1508. doi: 10.3934/dcds.2010.26.1491
[5]

Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264
[6]

Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515
[7]

Yanqing Wang. A semidiscrete Galerkin scheme for backward stochastic parabolic differential equations. Mathematical Control & Related Fields, 2016, 6 (3) : 489-515. doi: 10.3934/mcrf.2016013
[8]

Min Yang, Guanggan Chen. Finite dimensional reducing and smooth approximating for a class of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1565-1581. doi: 10.3934/dcdsb.2019240
[9]

Qi Lü, Xu Zhang. A concise introduction to control theory for stochastic partial differential equations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021020
[10]

Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295
[11]

Sergio Albeverio, Sonia Mazzucchi. Infinite dimensional integrals and partial differential equations for stochastic and quantum phenomena. Journal of Geometric Mechanics, 2019, 11 (2) : 123-137. doi: 10.3934/jgm.2019006
[12]

Tomasz Kosmala, Markus Riedle. Variational solutions of stochastic partial differential equations with cylindrical Lévy noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2879-2898. doi: 10.3934/dcdsb.2020209
[13]

Zhongkai Guo. Invariant foliations for stochastic partial differential equations with dynamic boundary conditions. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5203-5219. doi: 10.3934/dcds.2015.35.5203
[14]

Mogtaba Mohammed, Mamadou Sango. Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing. Networks & Heterogeneous Media, 2019, 14 (2) : 341-369. doi: 10.3934/nhm.2019014
[15]

Kexue Li, Jigen Peng, Junxiong Jia. Explosive solutions of parabolic stochastic partial differential equations with lévy noise. Discrete & Continuous Dynamical Systems, 2017, 37 (10) : 5105-5125. doi: 10.3934/dcds.2017221
[16]

Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5337-5354. doi: 10.3934/dcdsb.2019061
[17]

Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2021, 11 (4) : 797-828. doi: 10.3934/mcrf.2020047
[18]

Rongmei Cao, Jiangong You. The existence of integrable invariant manifolds of Hamiltonian partial differential equations. Discrete & Continuous Dynamical Systems, 2006, 16 (1) : 227-234. doi: 10.3934/dcds.2006.16.227
[19]

Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192
[20]

Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4927-4962. doi: 10.3934/dcdsb.2020320

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (102)
  • HTML views (0)
  • Cited by (19)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy