"Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$

Zdzislaw Brzezniak; Elżbieta Motyl

doi:10.1137/17M1111589

"Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$

Zdzislaw Brzezniak, Elżbieta Motyl

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A stochastic fractionally dissipative quasi-geostrophic type equation on ${\mathbb{R}}^{d}$ with a multiplicative Gaussian noise is considered.
We prove the existence of a martingale solution.
The construction of the solution is based on appropriate approximations,
the compactness method, and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.
In the 2D sub-critical case we also prove the pathwise uniqueness of the solutions.

Original language	English
Number of pages	55
Journal	SIAM journal on mathematical analysis
Early online date	4 Jun 2019
DOIs	https://doi.org/10.1137/17M1111589
Publication status	E-pub ahead of print - 4 Jun 2019

Bibliographical note

Keywords

Stochastic quasi-geostrophic equations
fractional Laplacian
martingale solution
pathwise uniqueness
Bessel potential

Access to Document

10.1137/17M1111589

QGE_Rd_SIMA_March_09_2019-ZB-EM
© 2019, Society for Industrial and Applied Mathematics
Accepted author manuscript, 206 KB

Cite this

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abstract = "A stochastic fractionally dissipative quasi-geostrophic type equation on ${\mathbb{R}}^{d}$ with a multiplicative Gaussian noise is considered.We prove the existence of a martingale solution.The construction of the solution is based on appropriate approximations, the compactness method, and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.In the 2D sub-critical case we also prove the pathwise uniqueness of the solutions.",

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N2 - A stochastic fractionally dissipative quasi-geostrophic type equation on ${\mathbb{R}}^{d}$ with a multiplicative Gaussian noise is considered.We prove the existence of a martingale solution.The construction of the solution is based on appropriate approximations, the compactness method, and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.In the 2D sub-critical case we also prove the pathwise uniqueness of the solutions.

AB - A stochastic fractionally dissipative quasi-geostrophic type equation on ${\mathbb{R}}^{d}$ with a multiplicative Gaussian noise is considered.We prove the existence of a martingale solution.The construction of the solution is based on appropriate approximations, the compactness method, and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.In the 2D sub-critical case we also prove the pathwise uniqueness of the solutions.

KW - Stochastic quasi-geostrophic equations

KW - fractional Laplacian

KW - martingale solution

KW - pathwise uniqueness

KW - Bessel potential

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