Research output: Contribution to journal › Article

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

Research output: Contribution to journal › Article

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

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

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

@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",

}

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 -