A framework for linear viscous gradient fluids as extensions of the Navier–Stokes law is derived. More precisely, the list of the independent variables is enlarged up to an Nth-order velocity gradient and, accordingly, also the list of the dependent variables up to dual hyperstress tensors of the same rank. It is shown that due to general invariance requirements, such models must be hemitropic functions. A complete representation for a second-order linear fluid and its balance equation are derived from a dissipation potential. In doing so, we follow Trostel (in: Trostel (ed) Beiträge zu den Ingenieurwissenschaften, Universitäts-Bibliothek der Technische Universität Berlin, Berlin, 96–134, 1985) and coworkers.

中文翻译：

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在粘性梯度流体上

得出了线性粘性梯度流体作为Navier–Stokes定律的扩展的框架。更精确地，自变量的列表被扩大到N阶速度梯度，因此，因变量的列表也被扩大到相同等级的双超应力张量。结果表明，由于一般不变性要求，这种模型必须是半同函数的。二阶线性流体的完整表示及其平衡方程是从耗散势得出的。在此过程中，我们遵循Trostel（在Trostel（ed）Beiträgezu den Ingenieurwissenschaften，柏林工业大学，柏林，柏林96-134，1985年）及其同事。