On the Stokes operator in general unbounded domains
On the Stokes operator in general unbounded domains
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DOI：
10.14492/hokmj/1248787007
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发表时间：
2009-02-01
影响因子：
0.5
通讯作者：
Sohr, Hermann
中科院分区：
文献类型：
--
作者：
Farwig, Reinhard;Kozono, Hideo;Sohr, Hermann
我们知道，在某些无界光滑区域的L-Q-空间中，除非q=2，否则Stokes算子不是良好定义的。本文将一般无界光滑区域的Stokes预解问题和最大正则性的一种新方法从三维情形推广到n维情形，n>；=2，将空间L-q，1<；q<；无穷代替空间L-q，1<；q<；无穷，其中(L)在bar(Q)上=L-q布尔，L-2对q>；=2和(L)在BAR(Q)=L-Q+L-2上1<；q<；2.特别地，我们证明了对于R-n，n>；=2中的一致C-1，C-1型无界区域，Stokes算子在Lq中是良好定义的，满足经典的预解估计，生成一个解析半群，并且具有极大正则性.
It is known that the Stokes operator is not well-defined in L-q-spaces for certain unbounded smooth domains unless q = 2. In this paper, we generalize a new approach to the Stokes resolvent problem and to maximal regularity in general unbounded smooth domains from the three-dimensional case, see [7], to the n-dimensional one, n >= 2, replacing the space L-q, 1 < q < infinity by (L) over bar (q) where (L) over bar = L-q boolean AND L-2 for q >= 2 and (L) over bar (q) = L-q + L-2 for 1 < q < 2. In particular, we show that the Stokes operator is well-defined in Lq for every unbounded domain of uniform C-1,C-1-type in R-n, n >= 2, satisfies the classical resolvent estimate, generates an analytic semigroup and has maximal regularity.