We prove the existence of continuous weak solutions of the nonlinear equations describing steady-state flows of second-grade fluids in a bounded three-dimensional domain under the no-slip boundary condition. A weak solution is found using the Galerkin method with special basis functions constructed with the help of a perturbed Stokes operator. An energy inequality for the resulting solution is derived.

中文翻译：

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二级流体稳态流动方程的弱可解性

我们证明了在无滑移边界条件下，在有界三维域中描述二级流体稳态流动的非线性方程的连续弱解的存在。使用 Galerkin 方法找到一个弱解，该方法具有在扰动斯托克斯算子的帮助下构造的特殊基函数。得出结果解的能量不等式。