Sub-critical and critical stochastic quasi-geostrophic equations with infinite delay

Tongtong Liang; Yejuan Wang

doi:10.3934/dcdsb.2020309

Article Contents

2021, Volume 26, Issue 9: 4697-4726. Doi: 10.3934/dcdsb.2020309

This issue Previous Article Non-autonomous stochastic evolution equations of parabolic type with nonlocal initial conditions Next Article Existence-uniqueness and stability of the mild periodic solutions to a class of delayed stochastic partial differential equations and its applications

Sub-critical and critical stochastic quasi-geostrophic equations with infinite delay

Tongtong Liang and
Yejuan Wang^,

School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China

^* Corresponding author
^* Corresponding author

Received: June 2020

Revised: September 2020

Early access: October 2020

Published: September 2021

This work was supported by the National Natural Science Foundation of China under grant 41875084

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Abstract

In this paper, we investigate a stochastic fractionally dissipative quasi-geostrophic equation driven by a multiplicative white noise, whose external forces contain hereditary characteristics. The existence and uniqueness of both local martingale and local pathwise solutions are established in $ H^s $ with $ s\geq2-2\alpha $, where $ \alpha\in(\frac{1}{2}, 1) $. For the critical case $ \alpha = \frac12 $, we obtain the similar results in $ H^s $ with $ s>1 $.

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Mathematics Subject Classification: Primary: 35Q86, 60H15, 76B03.

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