Classical Solution to the Navier-Stokes System
Classical Solution to the Navier-Stokes System
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纳维-斯托克斯系统的经典解
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发表时间：
1995
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通讯作者：
P. Maremonti
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作者：
P. Maremonti
本文在Ω （n = 2,3）中考虑平稳Navier-Stokes系统的边值问题。域Ω是一个有界域，假设其边界∂Ω属于c2类。到目前为止（cf. Galdi, 1994; Ladyzhenskaya, 1969），边值问题已经考虑假设边界数据a.(x)在∂Ω上具有适当的可微性(通常假设a （x)∈H 1/2（∂Ω））。这里我们试图给出一个存在性定理，而不需要对a(x)做这些假设。事实上，我们证明了在a(x)∈C（∂Ω）的唯一假设下，边值问题允许光滑解(v(x),π(x))∈c2 （Ω） C（（ar{Omega}）） × c1 （Ω）。
In this paper we consider in Ω ⊂ ℝ n (n = 2, 3) the boundary-value problem for the stationary Navier-Stokes system. The domain Ω is a bounded domain, whose boundary ∂Ω is assumed to be of class C 2 . So far (cf. Galdi, 1994; Ladyzhenskaya, 1969) the boundary-value problem has been considered assuming that the boundary data a.(x) has suitable properties of differentiability on ∂Ω (usually it is assumed that a (x) ∈ H 1/2 (∂Ω)). Here we try to give an existence theorem without making these assumptions on a(x). In fact, we prove that the boundary-value problem admits smooth solutions (v(x),π(x)) ∈C 2(Ω) ⋂ C(( ar{Omega } )) × C 1(Ω) under the sole hypothesis that a(x) ∈C(∂Ω).