On the Production of Dissipation by Interaction of Forced Oscillating Waves in Fluid Dynamics

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In the context of some bidimensionnal Navier-Stokes model, we exhibit a family of exact oscillating solutions {uε}ε defined on some strip [0,T]ײ which does not depend on ε∈]0,1]. The exact solutions is described thanks to a complete expansions which reveal a boundary layer in time t=0. The interactions of the various scales (1, 1/ε and 1/ε²) produce a macroscopic effect given by the addition of a diffusion. To justify the existence of {uε}ε, we need to perform various Sobolev estimates that rely on a refined balance between the informations coming from the hyperbolic and parabolic parts of the equations.