The generalized Navier–Stokes–Landau–Lifshitz equations are considered in this paper. The well-posedness for the multi-dimensional hyperviscous Navier–Stokes–Landau–Lifshitz equations is proved for \(n\ge 3\). The existence and uniqueness of the strong solutions for the generalized Navier–Stokes–Landau–Lifshitz equations are proved for \(\frac{5}{4}\le \alpha <\frac{5}{2}\) and \(\frac{5}{4}\le \beta <\frac{5}{2}\).

中文翻译：

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Navier–Stokes–Landau–Lifshitz方程的适定性

本文考虑了广义的Navier–Stokes–Landau–Lifshitz方程。证明了针对（（n \ ge 3 \）的多维超粘性Navier–Stokes–Landau–Lifshitz方程的适定性。证明了针对（（frac {5} {4} \ le \ alpha <\ frac {5} {2} \）和\（\）的广义Navier–Stokes–Landau–Lifshitz方程的强解的存在性和唯一性。\ frac {5} {4} \ le \ beta <\ frac {5} {2} \）。