On a free boundary problem for the Navier-Stokes equations
On a free boundary problem for the Navier-Stokes equations
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DOI：
10.57262/die/1356039501
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发表时间：
2007-01
影响因子：
1.4
通讯作者：
Y. Shibata;Senjo Shimizu
中科院分区：
文献类型：
--
作者：
Y. Shibata;Senjo Shimizu
本文考虑了空间$\mathbb{R}^{n}（n\geq 2）$中具有表面张力的多区域Navier-Stokes方程的自由边界问题.在空间$W_{q，p}^{2，1}$（2<p<\infty$ and $n<q<\infty）$中给出了一个局部时间唯一存在定理，并利用相应线性化问题的极大正则性定理证明了该定理.给出了相应线性化问题的预解式估计、解析半群的生成及极大正则性定理。
In this note, we consider a free boundary problem for tbe Navier-Stokes equation in several domains in $\mathbb{R}^{n}(n\geq 2)$ with surface tension. We will state a local in time unique existence theorem in the space $W_{q,p}^{2,1}$ $(2<p<\infty$ and $n<q<\infty)$ , which is proved by using the maximal regularity theorem of the corresponding linearized problem. Also, we state the resolvent estimate, the generation of analytic semigroup and the maximal regularity theorem of the corresponding linearized problem.