publication . Other literature type . Article . Preprint . 2018

On the small-time asymptotics of 3D stochastic primitive equations

Zhao Dong; Rangrang Zhang;
  • Published: 10 Jul 2018
  • Publisher: Wiley
Abstract
In this paper, we establish a small time large deviation principle for the strong solution of 3D stochastic primitive equations driven by multiplicative noise. Both the small noise and the small, but highly nonlinear, unbounded nonlinear terms should be taken into consideration.
Subjects
ACM Computing Classification System: MathematicsofComputing_NUMERICALANALYSIS
free text keywords: General Engineering, General Mathematics, Asymptotic analysis, Primitive equations, Large deviations theory, Mathematical analysis, Mathematics, Mathematics - Probability, 60F10, 60H15, 60G40
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18 references, page 1 of 2

[1] M.T. Barlow and M. Yor. Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local time. J. Funct. Anal. 49 198-229 (1982). [OpenAIRE]

[2] C. Cao, E.S. Titi: Global well-posedness of the three-dimensional viscous primitive equations of large-scale ocean and atmosphere dynamics. Ann. of Math. 166, 245-267 (2007). [OpenAIRE]

[3] G. Da Prato and J. Zabczyk. Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press, Cambridge, 1992.

[4] B. Davis. On the Lp norms of stochastic integrals and other martingales. Duke Math. J. 43 697-704 (1976).

[5] A. Debussche, N. Glatt-Holtz, R. Temam: Local martingale and pathwise solutions for an abstract fluids model. Physical D, 240, 1123-1144 (2011). [OpenAIRE]

[6] A. Debussche, N. Glatt-Holtz, R. Temam, M. Ziane: Global existence and regularity for the 3D stochastic primitive equations of the ocean and atmosphere with multiplicative white noise. Nonlinearity, 25, 2093-2118 (2012). [OpenAIRE]

[7] A. Dembo, O. Zeitouni: Large deviations techniques and applications. Jones and Bartlett, Boston, (1993).

[8] Z. Dong, J. Zhai, R. Zhang: Exponential mixing for 3D stochastic primitive equations of the large scale ocean. preprint. Available at arXiv: 1506.08514.

[9] Z. Dong, J. Zhai, R. Zhang: Large deviation principles for 3D stochastic primitive equations. preprint. Available at arXiv:1606.03677.

[10] H. Gao, C. Sun: Well-posedness and large deviations for the stochastic primitive equations in two space dimensions. Commun. Math. Sci. Vol.10, No.2, 575-593 (2012).

[11] B. Guo, D. Huang: 3D stochastic primitive equations of the large-scale ocean: global wellposedness and attractors . Comm. Math. Phys. 286, no. 2, 697-723 (2009).

[12] J.L. Lions, R. Temam, S. Wang: New formulations of the primitive equations of atmosphere and applications. Nonlinearity 5, 237-288 (1992). [OpenAIRE]

[13] J.L. Lions, R. Temam, S. Wang: On the equations of the large scale ocean. Nonlinearity 5, 1007- 1053 (1992). [OpenAIRE]

[14] J.L. Lions, R. Temam, S. Wang: Models of the coupled atmosphere and ocean. Computational Mechanics Advance 1, 1-54 (1993).

[15] J.L. Lions, R. Temam, S. Wang: Mathematical theory for the coupled atmosphere-ocean models. J. Math. Pures Appl. 74, 105-163 (1995).

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publication . Other literature type . Article . Preprint . 2018

On the small-time asymptotics of 3D stochastic primitive equations

Zhao Dong; Rangrang Zhang;