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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jiahui Zhu & Xinyun Wang & Heling Su, 2023. "Stochastic Quasi-Geostrophic Equation with Jump Noise in L p Spaces," Mathematics, MDPI, vol. 11(22), pages 1-17, November.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4608-:d:1277997
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