In this paper, we consider a steady MHD fluid model of non-Newtonian type in a smooth bounded domain \(\Omega \in {\mathbb {R}}^3\). Using the iterative method, under the condition that the external force is small in a suitable sense, we proved the existence of \(C^{1,\gamma }({\bar{\Omega }})\times W^{2,r}(\Omega )\) solutions of the systems for the exponent \(1<p<2\) and we show that this solution is unique in case \(\frac{6}{5}<p<2\). Moreover, we also proved the higher regularity properties of this solution.

中文翻译：

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一类非牛顿型MHD方程解的存在性，唯一性和正则性

在本文中，我们考虑在光滑有界域\（\ Omega \ in {\ mathbb {R}} ^ 3 \）中的非牛顿型稳定MHD流体模型。使用迭代方法，在适当的外力较小的条件下，我们证明存在\（C ^ {1，\ gamma}（{\ bar {\ Omega}}）\ W W {{2 ，r}（\ Omega）\）指数\（1 <p <2 \）的系统解，我们证明了在\（\ frac {6} {5} <p <2 \ ）。此外，我们还证明了该解决方案的较高规则性。