This paper is devoted to the stationary problem of second-grade fluids, in the case where #alpha#_1 + #alpha#_2 = 0, in three dimensions. In relation to the problem in two dimensions, studied by E. H. Ouazar, the H~3 norm of the velocity, in three dimensions, is not bounded for all data. However, by a special method, using together a H~1 bound of the velocity, a 'pseudo-continuous dependence' with respect to the data (effective for a small H~3 norm of the velocity) and a polynomial inequality (verified by the H~3 norm of the velocity), we show existence of solutions, uniqueness, continuous dependence with respect to the data, with small data. We also prove further regularity results establishing that this is a classical solution when the datum is small enough and smooth enough.
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机译：本文致力于在二维中＃alpha＃_1 +＃alpha＃_2 = 0的情况下二级流体的平稳问题。关于由E. H. Ouazar研究的二维问题，速度的H〜3范数在三个维度上并不适用于所有数据。但是，通过一种特殊的方法，将速度的H〜1界线，关于数据的“伪连续相关性”（对于速度的小H〜3范数有效）和多项式不等式（通过（速度的H〜3范数），我们显示出解的存在，唯一性，对数据的连续依赖性以及小数据。我们还证明了进一步的规律性结果，证明了当基准面足够小且足够光滑时，这是一种经典的解决方案。
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