Vanishing viscosity limit of the 3D incompressible Oldroyd-B model

Abstract

Consider the vanishing viscosity limit of the 3D incompressible Oldroyd-B model. It is shown that this set of equations admits a unique global solution with small analytic data uniformly in the coupling parameter ω close to 1 that corresponds to the inviscid case. We justify the limit from the Oldroyd-B model to the inviscid case \omega = 1 for all time. Moreover, if the nonlinear term g_{\alpha }(\tau ,\mathrm{∇}u) is ignored, similar results hold without resorting to the analytic regularity.

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