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

Zdzislaw Brzezniak, Elżbieta Motyl

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Number of pages55
JournalSIAM journal on mathematical analysis
Early online date4 Jun 2019
Publication statusE-pub ahead of print - 4 Jun 2019

Bibliographical note

© 2019, Society for Industrial and Applied Mathematics


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

Cite this