2018年6月2日
Paracontrolled quasi-geostrophic equation with space-time white noise
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- 記述言語
- 英語
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- 機関テクニカルレポート，技術報告書，プレプリント等
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.
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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- ID情報
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- arXiv ID : arXiv:1806.00564