On the Stokes problem in exterior domains: The maximum modulus theorem
On the Stokes problem in exterior domains: The maximum modulus theorem
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外域斯托克斯问题：最大模量定理
DOI：
10.3934/dcds.2014.34.2135
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发表时间：
2013
影响因子：
1.1
通讯作者：
P. Maremonti
中科院分区：
文献类型：
--
作者：
P. Maremonti
我们研究 Stokes 初始边值问题，
$(0,T) \times Ω$，其中 $Ω \subseteq \mathbb{R}^n$、$n\geq3$ 是外数
域，假设初始数据属于$L^\infty(Ω)$
并且在弱意义上具有零散度。我们证明最大模量
定理求出相应的解。对于证明至关重要
该结果与 Abe-Giga 对于有界证明的类似结果
域。我们的证明是通过对偶论证并采用
定义于上的解析算子的半群性质
$L^1(Ω)$。我们的结果与Solonnikov证明的结果相似
借助势能理论。
We study the Stokes initial boundary value problem, in
$(0,T) \times Ω$, where $Ω \subseteq \mathbb{R}^n$, $n\geq3$, is an exterior
domain, assuming that the initial data belongs to $L^\infty(Ω)$
and has null divergence in weak sense. We prove the maximum modulus
theorem for the corresponding solutions. Crucial for the proof of
this result is the analogous one proved by Abe-Giga for bounded
domains. Our proof is developed by duality arguments and employing
the semigroup properties of the resolving operator defined on
$L^1(Ω)$. Our results are similar to the ones proved by Solonnikov
by means of the potential theory.