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Chemetov, Nikolai, and Fernanda Cipriano. "THE INVISCID LIMIT FOR SLIP BOUNDARY CONDITIONS." HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS. Eds. F. Ancona, A. Bressan, P. Marcati, and A. Marson. Vol. 8. {AIMS Series on Applied Mathematics}, 8. PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA: Univ Padova, Dipartimento Matematica; Univ Studi Aquila, Dipartimento Matematica Pura Applicata; Univ Padova; Univ Zurich; Univ Basel, 2014. 431-438. Abstract

We study the inviscid limit for the two dimensional Navier-Stokes equations with non-homogeneous Navier slip boundary condition. We show that the vanishing viscosity limit of Navier-Stokes's solutions verifies the Euler equations with the corresponding Navier slip boundary condition just on the inflow boundary. The convergence result is established with respect to the strong topology of the Sobolev spaces W-p(1), p > 2.

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Mendes, Vilela R., and Fernanda Cipriano. "A stochastic representation for the Poisson-Vlasov equation." COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 13 (2008): 221-226. Abstract

{A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence proof and an intuitive characterization of the solutions, may also be used to obtain an intrinsic definition of the fluctuations. (c) 2007 Elsevier B.V. All rights reserved.}