Analyticity of the semigroup associated with the fluid–rigid body problem and local existence of strong solutions
Analyticity of the semigroup associated with the fluid–rigid body problem and local existence of strong solutions
复制标题
DOI：
10.1016/j.jfa.2011.07.001
复制
发表时间：
2011-11
影响因子：
1.7
通讯作者：
Yun Wang;Z. Xin
中科院分区：
文献类型：
--
作者：
Yun Wang;Z. Xin
本文研究了流体-刚体问题中的线性算子。算子最早是由T. Takahashi和M. Tucsnak（2004）[22].对于一般的三维情形，我们证明了相应的半群在L 65（R3）<$Lp（R3）（p <$2）上是解析的.特别地，当固体是R3中的球时，相应的半群在L2（R3）<$Lp（R3）（p <$6）上解析。在这种情况下，得到了流体-刚体问题唯一的局部强解。
In this paper, we study the linear operator associated with the fluid–rigid body problem. The operator was first introduced by T. Takahashi and M. Tucsnak (2004) [22]. For the general three-dimensional case, we prove that the corresponding semigroup is analytic on L65(R3)∩Lp(R3)(p⩾2). In particular, when the solid is a ball in R3, the corresponding semigroup is analytic on L2(R3)∩Lp(R3)(p⩾6). And for this case, a unique local strong solution to the fluid–rigid body problem is derived.