Paracontrolled quasi-geostrophic equation with space-time white noise

Yuzuru Inahama; Yoshihiro Sawano

Paracontrolled quasi-geostrophic equation with space-time white noise

Probability 2020-07-30 v3

Authors: Yuzuru Inahama , Yoshihiro Sawano

Abstract

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.

Keywords

stochastic quasi-geostrophic equation space-time white noise paracontrolled calculus ill-posed equation fractional laplacian local well-posedness

Cite

@article{arxiv.1806.00564,
  title  = {Paracontrolled quasi-geostrophic equation with space-time white noise},
  author = {Yuzuru Inahama and Yoshihiro Sawano},
  journal= {arXiv preprint arXiv:1806.00564},
  year   = {2020}
}

Comments

Final version. To appear in Dissertationes Math. 69 pages, no figure. Some typos were fixed

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