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.
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 |
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Number of pages | 55 |
Journal | SIAM journal on mathematical analysis |
Early online date | 4 Jun 2019 |
DOIs | |
Publication status | E-pub ahead of print - 4 Jun 2019 |
Bibliographical note
© 2019, Society for Industrial and Applied MathematicsKeywords
- Stochastic quasi-geostrophic equations
- fractional Laplacian
- martingale solution
- pathwise uniqueness
- Bessel potential