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The aim of this chapter is twofold: we will present in Sect. 5.3, in a concise way, a method to prove the well-posedness for 2-dimensional stochastic fluid dynamical equations introduced by Breckner (J. Appl. Math. Stoch. Anal 13(3):239–259, 2000) for Navier-Stokes equations with multiplicative noise with particular regularity properties, but well-suited to treat also different fluid dynamic systems and transport noise, which a priori does not satisfy the general assumptions of Breckner (J. Appl. Math. Stoch. Anal 13(3):239–259, 2000, Section 2).

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Well-Posedness and Inviscid Limit Results for Stochastic Second-Grade Fluid Equations with Transport Noise in Bounded Domains

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  • 发表日期：

    2025年

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  • Eliseo Luongo

摘要

The aim of this chapter is twofold: we will present in Sect. 5.3, in a concise way, a method to prove the well-posedness for 2-dimensional stochastic fluid dynamical equations introduced by Breckner (J. Appl. Math. Stoch. Anal 13(3):239–259, 2000) for Navier-Stokes equations with multiplicative noise with particular regularity properties, but well-suited to treat also different fluid dynamic systems and transport noise, which a priori does not satisfy the general assumptions of Breckner (J. Appl. Math. Stoch. Anal 13(3):239–259, 2000, Section 2).