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Chemetov, Nikolai, and Fernanda Cipriano. "Injection-suction control for two-dimensional Navier-Stokes equations with slippage." SIAM JOURNAL ON CONTROL AND OPTIMIZATION. 56 (2018): 1253-1281. Abstract

{We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.}

Cipriano, Fernanda, and Ivan Torrecilla. "Inviscid limit for 2D stochastic Navier-Stokes equations." STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 125 (2015): 2405-2426. Abstract

{We consider stochastic Navier-Stokes equations in a 2D-bounded domain with the Navier with friction boundary condition. We establish the existence and the uniqueness of the solutions and study the vanishing viscosity limit. More precisely, we prove that solutions of stochastic Navier Stokes equations converge, as the viscosity goes to zero, to solutions of the corresponding stochastic Euler equations. (C) 2015 Elsevier B.V. All rights reserved.}

Chemetov, N. V., and F. Cipriano. "Inviscid limit for Navier-Stokes equations in domains with permeable boundaries." Appl. Math. Lett.. 33 (2014): 6-11. Abstract

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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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Chemetov, N. V., and F. Cipriano. "The Inviscid Limit for the Navier-Stokes Equations with Slip Condition on Permeable Walls." JOURNAL OF NONLINEAR SCIENCE. 23 (2013): 731-750. Abstract

{We consider the Navier-Stokes equations in a 2D-bounded domain with general non-homogeneous Navier slip boundary conditions prescribed on permeable boundaries, and study the vanishing viscosity limit. We prove that solutions of the Navier-Stokes equations converge to solutions of the Euler equations satisfying the same Navier slip boundary condition on the inflow region of the boundary. The convergence is strong in Sobolev's spaces , which correspond to the spaces of the data.}