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- W4306292271 abstract "We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of L'evy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D Magnetic Bernard problem, and several Shell models of turbulence. In the existing literature on this topic, besides the classical Lipschitz and one sided linear growth conditions, other assumptions, which might be untypical, are also required on the coefficients of the stochastic perturbations. This paper is to get rid of these untypical assumptions. Our assumption on the coefficients of stochastic perturbations is new even for the Wiener cases, and in some sense, is shown to be quite sharp. A new cutting-off argument and energy estimation procedure play an important role in establishing the existence and uniqueness under this assumption." @default.
- W4306292271 created "2022-10-15" @default.
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- W4306292271 date "2020-05-09" @default.
- W4306292271 modified "2023-09-27" @default.
- W4306292271 title "Well-posedness of Stochastic 2D Hydrodynamics type Systems with Multiplicative L'evy Noises" @default.
- W4306292271 doi "https://doi.org/10.48550/arxiv.2005.04476" @default.
- W4306292271 hasPublicationYear "2020" @default.
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