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Paracontrolled quasi-geostrophic equation with space-time white noise

Volume 558 / 2020

Yuzuru Inahama, Yoshihiro Sawano Dissertationes Mathematicae 558 (2020), 1-81 DOI: 10.4064/dm806-7-2020 Published online: 13 November 2020


We study the stochastic dissipative quasi-geostrophic equation with space-time white noise on the two-dimensional torus. This equation is highly singular and basically ill-posed in its original form. The main objective of the present paper is to formulate and solve this equation locally in time in the framework of paracontrolled calculus when the differential order of the main term, the fractional Laplacian, is larger than $7/4$. No renormalization has to be done for this model.


  • Yuzuru InahamaFaculty of Mathematics
    Kyushu University
    Motooka 744, Nishi-ku, Fukuoka
    819-0395, Japan
  • Yoshihiro SawanoDepartment of Mathematics
    Chuo University
    1-13-27, Kasuga, Bunkyo, Tokyo
    112-8551, Japan

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