In this paper, we derive an incompressible Oldroyd-B model with hybrid dissipation and partial damping on stress tensor $$\tau $$ τ via the velocity equations and the generalized constitutive law so that global well-posedness of the model is established in the Sobolev space framework. Precisely speaking, the proof is based on the curl-div free property of $$\tau - {\nabla }\frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau - ( {\nabla } \frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau )^T $$ τ - ∇ 1 Δ P div τ - ( ∇ 1 Δ P div τ ) T , the low frequency dissipation and high frequency damping of $$\tau $$ τ and the dissipation of u .

中文翻译：

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具有混合耗散和应力张量部分阻尼的二维不可压缩 Oldroyd-B 模型的全局解

在本文中，我们通过速度方程和广义本构律推导出一个具有混合耗散和应力张量部分阻尼的不可压缩的 Oldroyd-B 模型索博列夫空间框架。准确地说，证明是基于 $$\tau - {\nabla }\frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau - ( {\nabla } \frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau )^T $$ τ - ∇ 1 Δ P div τ - ( ∇ 1 Δ P div τ ) T ，低频耗散和 $$\tau $$ τ 的高频阻尼和 u 的耗散。