We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p -Stokes and a q -Stokes stress tensor, with 1 < p <2 < q <∞. For a wide range of parameters ( p , q ), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors.

中文翻译：

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论稳态双相流体弱解的唯一性

我们考虑一种双相非牛顿流体，由一个应力张量描述，该张量是 ap -Stokes 和 aq -Stokes 应力张量之和，1 < p <2 < q <∞。对于广泛的参数（ p ， q ），我们证明了小解决方案的唯一性。我们使用 p < 2 特征来获得应力张量的二次型估计，而我们使用来自 q > 2 项的改进的规律性来证明弱解的计算是正确的。结果是通过仔细使用对流项的对称性获得的，并且对于相当普遍的（甚至各向异性的）应力张量也是有效的。