Stochastic Quasi-Geostrophic Equation with Jump Noise in L p Spaces

Jiahui Zhu (), Xinyun Wang and Heling Su
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Jiahui Zhu: School of Science, Zhejiang University of Technology, Hangzhou 310019, China
Xinyun Wang: School of Science, Zhejiang University of Technology, Hangzhou 310019, China
Heling Su: School of Science, Zhejiang University of Technology, Hangzhou 310019, China

Mathematics, 2023, vol. 11, issue 22, 1-17

Abstract: In this paper, we consider a 2D stochastic quasi-geostrophic equation driven by jump noise in a smooth bounded domain. We prove the local existence and uniqueness of mild L p ( D ) -solutions for the dissipative quasi-geostrophic equation with a full range of subcritical powers α ∈ ( 1 2 , 1 ] by using the semigroup theory and fixed point theorem. Our approach, based on the Yosida approximation argument and Itô formula for the Banach space valued processes, allows for establishing some uniform bounds for the mild solutions and we prove the global existence of mild solutions in L ∞ ( 0 , T ; L p ( D ) ) space for all p > 2 2 α − 1 , which is consistent with the deterministic case.

Keywords: Poisson random measure; stochastic quasi-geostrophic equation; global mild solution; semigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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