TY - JOUR
T1 - Dissertationes mathematicae
AU - Inahama, Yuzuru
AU - Sawano, Yoshihiro
N1 - Funding Information:
The research of Y. Inahama was partially supported by Grant-in-Aid for Scientific Research (C) (15K04922), the Japan Society for the Promotion of Science. The research of Y. Sawano was partially supported by Grant-in-Aid for Scientific Research (C) (16K05209), the Japan Society for the Promotion of Science, and also by Department of Mathematics Analysis and the Theory of functions, Peoples’ Friendship University of Russia, Moscow, Russia.
Publisher Copyright:
© by Instytut Matematyczny PAN, Warszawa 2020.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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U2 - 10.4064/dm806-7-2020
DO - 10.4064/dm806-7-2020
M3 - Article
AN - SCOPUS:85109157588
VL - 558
JO - Dissertationes Mathematicae
JF - Dissertationes Mathematicae
SN - 0012-3862
ER -