A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data
A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data
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非齐次数据纳维-斯托克斯方程的一类新弱解
DOI：
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发表时间：
2006
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通讯作者：
H. Sohr
中科院分区：
文献类型：
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作者：
R. Farwig;G. Galdi;H. Sohr
摘要：研究了有界区域上定常和非定常Navier-Stokes方程的一类弱解，即所谓的很弱解
$$Omega subseteq mathbb{R}^{3}$$。这个概念是由Amann [3]，[4]引入的，用于具有非齐次边界数据的非平稳情况，导致非常大的低正则性解类。这里我们主要研究具有任意散度k = div u，边界数据g = u的更一般问题的“最大可能”解类u| Ω和外力f，尽可能弱，但保持唯一性。原则上，我们将遵循阿曼的方法。
Abstract.We investigate a class of weak solutions, the so-called very weak solutions, to stationary and nonstationary Navier–Stokes equations in a bounded domain
$$Omega subseteq mathbb{R}^{3}$$. This notion was introduced by Amann [3], [4] for the nonstationary case with nonhomogeneous boundary data leading to a very large solution class of low regularity. Here we are mainly interested in the investigation of the “largest possible” class of solutions u for the more general problem with arbitrary divergence k = div u, boundary data g = u|∂Ω and an external force f, as weak as possible, but maintaining uniqueness. In principle, we will follow Amann’s approach.