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Author:

You, Bo (You, Bo.)

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Abstract:

The objective of this paper is to study the well-posedness of solutions for the three dimensional planetary geostrophic equations of large-scale ocean circulation with additive noise. Since strong coupling terms and the noise term create some difficulties in the process of showing the existence of weak solutions, we will first show the existence of weak solutions by the monotonicity methods when the initial data satisfies some "regular" condition. For the case of general initial data, we will establish the existence of weak solutions by taking a sequence of "regular" initial data and proving the convergence in probability as well as some weak convergence of the corresponding solution sequences. Finally, we establish the existence of weak D-pullback mean random attractors in the framework developed in [11, 25].

Keyword:

Additive noise Planetary geostrophic equations Weak D-pullback mean random attractors Well-posedness

Author Community:

  • [ 1 ] [You, Bo]Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

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Source :

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

ISSN: 1078-0947

Year: 2021

Issue: 4

Volume: 41

Page: 1579-1604

1 . 3 9 2

JCR@2020

ESI Discipline: MATHEMATICS;

ESI HC Threshold:13

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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