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Lp-solutions of the Navier-Stokes equation with fractional Brownian noise

1 Dipartimento di Matematica, Universitàdi Pavia, via Ferrata 5, 27100 Pavia, Italy
2 Departamento de Matemática, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, 13083-859 Campinas, SP, Brazil

Topical Section: Mathematical Analysis in Fluid Dynamics

We study the Navier-Stokes equations on a smooth bounded domain $D\subset \mathbb R^d$ ($d=2$ or 3), under the effect of an additive fractional Brownian noise. We show local existence and uniqueness of a mild $L^p$-solution for $p>d$.
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Keywords stochastic partial di erential equations; Navier-Stokes equations; mild solution; fractional Brownian motion

Citation: Benedetta Ferrario, Christian Olivera. Lp-solutions of the Navier-Stokes equation with fractional Brownian noise. AIMS Mathematics, 2018, 3(4): 539-553. doi: 10.3934/Math.2018.4.539

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