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

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"Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$. / Brzezniak, Zdzislaw; Motyl, Elżbieta.

In: SIAM journal on mathematical analysis, 04.06.2019.

Research output: Contribution to journalArticle

Harvard

Brzezniak, Z & Motyl, E 2019, '"Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$', SIAM journal on mathematical analysis. https://doi.org/10.1137/17M1111589

APA

Brzezniak, Z., & Motyl, E. (2019). "Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$. SIAM journal on mathematical analysis. https://doi.org/10.1137/17M1111589

Vancouver

Brzezniak Z, Motyl E. "Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$. SIAM journal on mathematical analysis. 2019 Jun 4. https://doi.org/10.1137/17M1111589

Author

Brzezniak, Zdzislaw ; Motyl, Elżbieta. / "Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$. In: SIAM journal on mathematical analysis. 2019.

Bibtex - Download

@article{5eaba640bf5f4bb19063346cee6e9b54,
title = "{"}Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$",
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.",
keywords = "Stochastic quasi-geostrophic equations, fractional Laplacian, martingale solution, pathwise uniqueness, Bessel potential",
author = "Zdzislaw Brzezniak and El{\.z}bieta Motyl",
note = "{\textcopyright} 2019, Society for Industrial and Applied Mathematics ",
year = "2019",
month = jun,
day = "4",
doi = "10.1137/17M1111589",
language = "English",
journal = "SIAM journal on mathematical analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - "Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$

AU - Brzezniak, Zdzislaw

AU - Motyl, Elżbieta

N1 - © 2019, Society for Industrial and Applied Mathematics

PY - 2019/6/4

Y1 - 2019/6/4

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

U2 - 10.1137/17M1111589

DO - 10.1137/17M1111589

M3 - Article

JO - SIAM journal on mathematical analysis

JF - SIAM journal on mathematical analysis

SN - 0036-1410

ER -