Quasigeostrophic equation with random initial data in negative-order Sobolev space

  • Lihuai Du
  • Huaqiao WangEmail author


This paper is concerned with the Cauchy problem of the Quasigeostrophic equation on the torus \({\mathbb {T}}^2\). We prove the almost sure existence and uniqueness of the global solution with the random initial data in \({\mathcal {H}}^s({\mathbb {T}}^2), s\in [-1,0)\).


Quasigeostrophic equation Random initial data Negative-order Sobolev space 

Mathematics Subject Classification

35Q35 76D03 



The authors express their sincere gratitude to the reviewers for their comments and suggestions. H. Wang’s research was supported by National Postdoctoral Program for Innovative Talents (No. BX201600020) and Project No. 2019CDXYST0015 supported by the Fundamental Research Funds for the Central Universities. L. Du’s research was supported by China Postdoctoral Science Foundation (No. 2019M650580).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Applied Physics and Computational MathematicsBeijingChina
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingChina

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