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

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JournalSIAM journal on mathematical analysis
DateAccepted/In press - 19 Feb 2019
DateE-pub ahead of print (current) - 4 Jun 2019
Number of pages55
Early online date4/06/19
Original languageEnglish

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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© 2019, Society for Industrial and Applied Mathematics

    Research areas

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

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