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arXiv 1111.2787math.AP
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具有临界奇异外力的定常Navier-斯托克斯方程解的存在性和稳定性

Stationary Navier-Stokes Equations with Critically Singular External Forces: Existence and Stability Results

Tuoc Van Phan, Nguyen Cong Phuc

摘要:

我们证明了在临界空间中具有小奇异外力的定常Navier-斯托克斯方程解的唯一存在性。据我们所知,这是迄今为止可用于这种存在的最大临界空间。这个结果可以看作是H. Koch和D.用BMO $^{-1}$中的初始数据求解自由非定常Navier-斯托克斯方程。通过对奇摄动算子和相应半群的预解式的一系列精确估计,得到了该空间中定态解的稳定性。

英文摘要:

We show the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces belonging to a critical space. To the best of our knowledge, this is the largest critical space that is available up to now for this kind of existence. This result can be viewed as the stationary counterpart of the existence result obtained by H. Koch and D. Tataru for the free non-stationary Navier-Stokes equations with initial data in BMO$^{-1}$. The stability of the stationary solutions in such spaces is also obtained by a series of sharp estimates for resolvents of a singularly perturbed operator and the corresponding semigroup.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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