Existence of Solutions to the Nonhomogeneous Steady Navier-Stokes Equations.
Existence of Solutions to the Nonhomogeneous Steady Navier-Stokes Equations.
复制标题
DOI：
10.21236/ada129171
复制
发表时间：
1983-04
期刊：
影响因子：
--
通讯作者：
C. Amick
中科院分区：
文献类型：
--
作者：
C. Amick
翻译后摘要：本文关注的是在有界区域的Navier-Stokes方程的稳定解的存在性。速度场的螺线管性条件对边界数据施加了一个必要条件。对于一类对称域，作者证明了这个必要条件蕴含着问题解的存在性。该方法包括证明先验界的解决方案，通过假设相反，重新调整方程，然后到达一个解决方案的稳定的欧拉方程的限制。对这个等式的考察导致了所期望的矛盾。在任何解有了合适的界之后，我们就用Leray-Schauder定理来证明解的存在性。此外，作者评论的问题，一般有界域，并建议如何某些最大值原则可能会产生预期的结果。
Abstract : This paper concerns the existence of steady solutions to the Navier-Stokes equations in a bounded domain. The condition of solenoidality for the velocity field imposes a necessary condition on the boundary data. For a certain class of symmetrical domains, the authors show that this necessary condition implies the existence of a solution to the problem. The method consists of proving a priori bounds on solutions by assuming the contrary, rescaling the equations, and then arriving at a solution to the steady Euler equations in the limit. Examination of this equation leads to the desired contradiction. After one has suitable bounds on any solutions, one uses the Leray-Schauder theorem to prove existence. In addition, the authors remark on the problem of a general bounded domain, and suggest how certain maximum principles might yield the expected results.