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 $g_{\alpha }(\tau ,\mathrm{\nabla }u)$ is ignored, similar results hold without resorting to the analytic regularity.

中文翻译：

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3D 不可压缩 Oldroyd-B 模型的消失粘度极限

考虑 3D 不可压缩 Oldroyd-B 模型的消失粘度极限。结果表明，这组方程在对应于无粘性情况的耦合参数ω接近 1 的情况下，承认具有小解析数据的唯一全局解。我们证明了从 Oldroyd-B 模型到无粘性情况的限制$\omega =1$一直以来。此外，如果非线性项$G_{\alpha }(\tau ,\mathrm{\nabla }你)$ 被忽略，类似的结果在不诉诸解析规律的情况下也成立。